Middlesex 254 for 3 (Eskinazi 73, Holden 68*, Higgins 48) beat Surrey 252 for 7 (Jacks 96, Evans 85) by seven wickets
Eskinazi blasted 73 from 39 balls, in an opening blitz of 90 runs in just 6.3 overs with Joe Cracknell, who made 36 off 16, before Holden took over with a nerveless 68 not out from 35 balls - adding 105 in 7.4 overs under the lights with Ryan Higgins.
Higgins, who had bowled well amid the carnage of Surrey's innings to take 2 for 40 - his ten runs per over making him the most economical bowler of the whole evening - batted superbly for his 48 off 24 balls, pulling the first ball he faced, from Chris Jordan, for six.
And when Higgins was caught behind off Jordan in the penultimate over, 23-year-old left hander Jack Davies came in to take a single to keep the strike for the last over before scooping Gus Atkinson for six over fine leg and then slicing another low full toss next ball for four to take his side to 253 for three and spark joyous scenes of jubilation in the Middlesex dug out.
This was Middlesex's first win in 15 T20 games, stretching back to last summer, and their incredible chase was the highest in Blast history and the second highest in T20 matches around the world.
But Jacks was left slightly annoyed, after thumping Luke Hollman for five sixes from the first five balls of the 11th over, that he could then only mishit a knee-high full toss from the leg spinner to deep mid wicket. "I don't think I'll get a better chance of hitting six sixes in an over than that so it's a little bit disappointing," said Jacks.
After crashing seven sixes and eight fours in all, Jacks was caught on the cover boundary off Martin Andersson going for yet another six to complete his hundred, and by then Evans had also been bowled swinging at 21-year-old paceman Max Harris to end a brilliant knock of his own featuring five sixes and nine fours.
The final part of Surrey's innings, just six runs short of their highest T20 total but their best against Middlesex, was a flurry of wickets and more big hits - if not at quite the rate achieved by Jacks and Evans.
There were further sixes, however, from both Jamie Overton (18) and Sean Abbott (11) before Jordan ended the innings in style by striking the first and final balls of Tom Helm's 20th over for sixes driven high and straight and pulled far over mid wicket to finish on 16 not out.
It meant that Surrey totalled 16 sixes and 19 fours in their thrilling onslaught on an excellent batting pitch after being put in by a Middlesex side that had lost their ten previous South Group matches this season, and the final four of last year's Blast competition.
So it was to their enormous credit that Middlesex, led by their skipper Eskinazi, responded with such bravery to the huge task in front of them. Eskinazi hit 14 fours and a six, swung over mid wicket off Abbott in a second over of the innings costing 20, and with Cracknell also striking it well the Middlesex total was a stunning 83 for no wicket at the end of the six-over powerplay. At halfway they were 129 for 1 and after 15 overs 200 for 2.
Cracknell was run out in an unfortunate mix-up but Holden struck Sunil Narine for a straight six and later took another maximum off the West Indian star spinner. In all, Middlesex hit eight sixes and no fewer than 33 fours on a truly spectacular night in south London.
What they said
Stephen Eskinazi
"It was an absolutely incredible game of cricket and although our celebrations at the end may have looked over the top it's because as a group of players, and staff, we have been through a phenomenally difficult period of time in this competition.
"Our feelings now are that this win is a vindication as a group that we are doing the right things even though we must have been on the longest losing streak that any team has had in T20 cricket. This is a really special evening and really special result, even though it's only our first win of the season."
Max Holden
"It's been a tricky time for everyone this summer in T20 but we still have believed we were building towards a performance like that. Results have not been going our way but we've felt there have been positives and so it's great now to get a victory like that. It was an amazing batting pitch and even when they got their total on the board we still did think we could do something special."
Chris Jordan
"We will look at areas where it went wrong for us tonight, and perhaps especially the way we started their innings. I don't think we hit the areas we wanted to hit in those early powerplay overs but full credit to Middlesex and the way they played to chase that down.
"They came hard at us all the way through their innings and that made it very difficult for us. T20 is a momentum game and they never gave it up after getting off to a flyer. They always had an answer to everything we tried and that's great credit to them."