Imperious Ireland dismantled Scotland with a display of clinical brilliance to reach the World Cup quarter-finals and send their opponents crashing out of the tournament.

Ireland got off to a dream start in Paris as James Lowe crashed over for the opening try after only two minutes.

The loss to injury of Blair Kinghorn and captain Jamie Ritchie further hampered the Scots before two more Hugo Keenan tries and one from Iain Henderson all but ended the contest by half-time.

Dan Sheehan and Garry Ringrose also touched down to rub salt into the Scottish wounds before replies from Ewan Ashman and Ali Price at least made the score more respectable.

Scotland's defeat means holders South Africa qualify as runners-up to face Pool A winners France.

This was a 17th straight victory for Ireland, a run that's beginning to look inexorable. They have seen them all off - the All Blacks, the Springboks, the French, the English and now the Scots, trampled mercilessly underfoot.

For all Scotland's big talk, this was a cruel rout, a systematic Irish dismantling and humiliation of a side who came here looking for an eight-point win that went from improbable to virtually impossible after a single minute.

Ireland were ruthless. They identified where the Scots were weak and they targeted them viciously.

They exposed the underdogs down the 13 channel, they went after them in the air and out of touch, they knew that Scotland's morale could collapse when behind and that they have a propensity to concede scores in clusters.

They showed power, imagination, clarity, accuracy, belief and a clinical edge.

Glorious to witness if you were one of the millions - or maybe it just sounded like there were millions - in green at the Stade and just about the most embarrassing experience any Scotland fan has endured in an age.

Irish power overwhelms hapless Scots

For the opener, the Scots were sucked in, their defence narrow, their resistance nowhere good enough to live with Ringrose, Mack Hansen and finally Lowe. Knives through butter. What a start for Ireland.

We then had waves of Scotland attacks, all met with outstanding Irish defence. The Scots won a penalty and went for touch instead of the posts, which was an odd call when you needed scoreboard pressure.

They won another kickable penalty and went to touch again. The imperious Peter O'Mahony, on his 100th cap, stole it.

They won a third kickable penalty and went through 18 phases of huff and puff. Their yardage was negative by the end of it. There was a green wall in front of them and there was no breaking through it.

The psychology of those moments was huge. The Scots had wasted chances to put points on board and the Irish had a chance to show how unbreakable their defence is as a consequence.

Scotland were done at that point. Fourteen minutes and it was all but over bar the Irish deluge, which came soon enough.

They had lost Blair Kinghorn to injury and now they lost their captain, Jamie Ritchie. It was a tartan horror show.

O'Mahony stole another line-out and Ireland went hunting again. From the next line-out, they threw a set-play move at the Scots that was like a razor blade.

Again, it was down the 13 channel. Sexton linked with Bundee Aki, who spooked Sione Tuipulotu and Jones to such an extent that both of them haplessly went for him, leaving Ringrose free to put Keenan away. Simple, beautiful and clinical.

Sexton's conversion made it 12-0, a prelude to a seven-minute spell at the end of the half when Irish forward power blasted through with ease.

Henderson thundered over, Sexton made it 19-0. This was men and boys. It looked like tier one against tier two for large parts.

Before the end of the half, Keenan scored again, Sexton finding him after close-range pressure. It was easy, oh so easy.

There wasn't a battle out there that Ireland weren't winning by a landslide. Ireland had scored 14 points in seven minutes and 26 in 40. Sensational.

Things only got better for them. Cranky, the Scots started a bit of a scrap on the touchline when Ollie Smith tripped Sexton and sparked a pile-on. Smith saw yellow and no sooner was he gone than Sheehan drove over to increase the pain.

Out the line they went, sucking in what existed of the Scottish cover, little pop passes, masses of deception, lovely angles and invention. Too much, way too much; 31-0.

And there was more. In the 49th minute, Farrell emptied his bench. Many of his high-rollers were brought off to save them for the quarter-final. The fact that it happened so early was another illustration of Ireland's utter dominance.

Even without the first-choice artillery, they scored again, Jack Crowley, on for Sexton, cross-kicked to the towering Ringrose, who had the simple job of dotting down in the left corner. Now it was 36-0. A message to the rugby world.

Scotland rallied and scored some consolations, not that it mattered. Ashman and Price ran away to score to make it 36-14 with Finn Russell's conversions.

Those tries raised a brief cheer from the Scottish ranks, but they were a shell-shocked lot. They came in hope rather than expectation, but they didn't anticipate a slaughter. They're heading home now, in disarray.

Another early exit from a World Cup. Another retreat to the world of recriminations.

Ireland will now play New Zealand, a team they'll respect but will not fear. They've beaten the All Blacks the last two times they've played them, they've won three of the last four and five of the last eight.

They believe, as do their supporters. The scenes at the end were remarkable, the stadium full of Irish noise and Irish colour. Powerful.

On roads and railways they moved as one earlier in the day, a sea of green.

There were many thousands of Scots in town, but they were outnumbered by a bewildering margin. World number one on the pitch and, quite obviously, world number one off it. This was an immense night for them.

New Zealand coach Ian Foster and Rassie Erasmus, the high-priest of South African rugby, attempted some trash talking during the week, some chat they hoped would unsettle Ireland before this contest.

Foster and Erasmus got their answer, as Scotland's bravado, got its answer, square between the eyes.

'It was a special performance' - what they said

Ireland head coach Andy Farrell: "I think it was a special performance because Scotland really came out of the blocks. They threw everything at us.

"I thought our attitude, our defence to try and keep them out for long spells was the making of the game. We were calm enough and clinical enough when we got back down the other end of the field to put some points on the board.

"As far as a quarter-final is concerned it doesn't get any tougher, the respect we have got for New Zealand is through the roof and hopefully they have got a bit of respect for us."

Scotland head coach Gregor Townsend: "They were very clinical, very accurate and I thought they put a huge effort in defensively when we had a bit of pressure in that first 20 minutes. They are an outstanding team.

"When you play the top teams, you've got to take your opportunities and we didn't do that in the first quarter.

"I'm proud of the effort in the second half. The game had gotten away from us, so we focused on winning back respect. To get two tries against such a top team, we'll take a little bit out of that."

Scotland captain Jamie Ritchie: "I'm really proud of how we've stuck together. We had a bit of hardship from the first game, proud of how we stayed in the fight today, we showed how we can score some points at the end."

"What we try to do is play our game - unfortunately it wasn't enough tonight and full credit to Ireland, that's probably the best I've seen them play."

Line-ups

Ireland: Keenan; M Hansen, Ringrose, Aki, Lowe; Sexton (capt), Gibson-Park; Porter, Sheehan, Furlong; Beirne, Henderson; O'Mahony, Van der Flier, Doris.

Replacements: Kelleher, Kilcoyne, Bealham, Ryan, Conan, Murray, Crowley, McCloskey.

Scotland: Kinghorn; Graham, Jones, Tuipulotu, Van der Merwe; Russell, Price; Schoeman, Turner, Fagerson, Gray, Gilchrist, Ritchie (capt), Darge, Dempsey.

Replacements: Ashman, Sutherland, Nel, Cummings, M Fagerson, Crosbie, Horne, Smith.