England survived a late red card for Manu Tuilagi to secure a first Triple Crown in four years and inflict a third successive defeat on new Wales head coach Wayne Pivac.
Cleverly worked first-half tries from Anthony Watson and Elliot Daly and a brace of penalties and conversions from Owen Farrell opened up an 11-point half-time lead, Wales' only points coming from three penalties.
Wales went the length of the pitch to score a sublime try through Justin Tipuric before England re-established command through Farrell's boot and a try from Tuilagi.
The England centre was then controversially sent off for a no-arms tackle on George North, and with Ellis Genge in the sin-bin England were down to 13 men.
Dan Biggar and then Tipuric again capitalised with late tries but England's lead was just big enough and they held on amidst the chaos.
With England's final game against Italy postponed because of the coronavirus, France remain favourites to win the championship.
But after defeat in Paris in their opening game, Eddie Jones' men have recaptured some of the form and momentum that took them to a World Cup final four months ago.
Fiery Farrell sparks for England
England came charging out of the blocks, Tom Curry flattening Dan Biggar from an early up-and-under, and Maro Itoje cantering deep into the Welsh 22.
And off clean line-out ball Ben Youngs found Watson on his inside, the winger stepping past two Welsh defenders to fight his way over the line.
Farrell banged over the conversion to go past 900 points for England, but after North had knocked on close to the England try-line after good work from Nick Tompkins, the England skipper was penalised for shoving North in the ruck, and Halfpenny made it 7-3.
A head injury to Jonny May after the winger went up for a high ball meant an early entry for replacement Henry Slade and a test of Jones' decision to select a bench with only one outside back.
Farrell and Halfpenny exchanged further successful penalties as the game became cagier and scrappier, but then England struck again.
From another penalty kicked to the corner England set up a driving maul, and Youngs went sniping only to be lassoed by a high tackle from Rob Evans.
With the penalty coming England went wide, Farrell and George Ford combining beautifully as Slade's dummy run created the space down the left for Daly to dive over through North's despairing tackle.
Wales were creaking, the penalties piling up and Farrell kicking another with unerring accuracy from 35 metres to make it 20-6.
Itoje went high on Biggar to give the Welsh fly-half the chance to cut that lead by three at the interval, Wales grateful to be within 11 points.
Tuilagi sees red as Tipuric inspires
England's lead was reduced within seconds of the kick-off as Wales conjured up one of the great Six Nations tries.
With England's kick-chase dawdling Tompkins set off from his own five-metre line, found Josh Navidi outside him and took the return pass on halfway before slipping it on to the supporting Tomos Williams on his inside.
And the scrum-half drew the last man Daly before setting Tipuric away to canter in from 25 metres and light up a grey afternoon.
With Biggar popping over the conversion it was suddenly a four-point game, and Wales' supporters were dreaming of another famous Twickenham heist.
But Courtney Lawes went digging at a ruck to win a penalty that Farrell stroked over, and Ford made it 26-16 as England's powerful forwards won a scrum penalty.
Jones threw on Joe Launchbury and Luke Cowan-Dickie and the power and points kept coming.
Youngs made another break, Watson and then the forwards took it on and with Welsh defenders sucked in Ford flipped a little pass away under pressure to let Tuilagi walk in his side's third try.
With Farrell curling over the conversion from out wide it was 33-16 and the game seemed safe.
But then Tuilagi was dismissed after a long discussion between referee Ben O'Keeffe and TMO Marius Jonker, and Wales were able to strike back before finally running out of time.
Man of the match: Ben Youngs
The England scrum-half is closing in on his 100th England cap and recaptured his running threat of old to keep his side constantly on the front foot.
'A brilliant performance' - what they said
England captain Owen Farrell speaking to Radio 5 Live: "I thought it was a brilliant performance. A few less players on the pitch at the end made it difficult, but in terms of effort and composure when they put us under pressure, it was brilliant. I thought people worked extremely hard to fight for the team."
Wales captain Alun Wyn Jones: "We're probably lamenting a couple of territorial giveaways in the first half. Then you are chasing the game a little bit.
"Unfortunately they capitalised on a couple of bits of indiscipline and kept the scoreboard at bay. Those two tries show what we can do but it was too little too late in the end."
Analysis
Former England scrum-half Matt Dawson: "England were disciplined in their tactics and execution. That wonder try from Wales at the beginning of the second half rocked England a bit, and they couldn't quite get back into their pattern.
"Wales played much, much better in the second half, they threw a bit of caution to wind. They were not going to win with the tactics they employed for the first 40 minutes. It would have been a genuinely nail-biting, tense last few minutes if they'd done that earlier."
Former Wales fly-half Jonathan Davies: "It was always going to be difficult after Warren Gatland left. Wales looked a little more dangerous, but they've got to learn to vary their tactics. England were always on the front foot."
Line-ups
England: Daly; Watson, Tuilagi, Farrell (capt), May; Ford, Youngs; Marler, George, Sinckler, Itoje, Kruis, Lawes, Wilson, Curry.
Replacements: Slade for May (8), Heinz for Youngs (70), Genge for Marler (66), Cowan-Dickie for George (58), Stuart for Sinckler (76), Launchbury for Kruis (58), Ewels for Lawes (66), Earl for Wilson (76).
Sin-bin: Genge (73).
Sent off: Tuilagi (75).
Wales: Halfpenny; North, Tompkins, Parkes, Williams; Biggar, 9-Tomos Williams; R Evans, Owens, Lewis, Ball, Jones (capt), Moriarty, Tipuric, Navidi.
Replacements: McNicholl for L. Williams (66), Webb for T. Williams (46), Carre for R. Evans (58), Elias for Owens (75), Brown for Lewis (41), Shingler for Ball (58), Faletau for Moriarty (58).
Referee: Ben O'Keeffe (New Zealand)
Touch judges: Romain Poite (France) & Alexandre Ruiz (France)
TMO: Marius Jonker (South Africa)
Phone: (800) 737. 6040
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