Middlesex 226 for 8 (Higgins 61, Critchley 5-28) beat Essex 225 for 6 (Sams 69*) by two wickets
The Middlesex all-rounder's 61 was plundered off just 24 balls and included three sixes and eight fours. It laid the foundations for a chase after 226 runs only surpassed by their record 253 to beat Surrey last week.
Essex now head to The Oval on Sunday where they must beat Surrey to stand any chance of a place in next week's quarter-finals.
Essex, put in, typically lost three wickets in the powerplay while creeping along to 52 runs. It was the calm before the storm. Feroze Khushi was first to go taking a swing at Ethan Bamber and picking out deep mid-off.
Adam Rossington, returning after a finger injury, hit two sixes, one ramped off Tom Helm, before edging behind for 19 off 13 balls.
Dan Lawrence completed the trio of early wickets when he retreated towards square leg against Josh De Caires and found himself stretching in vain as the ball thudded into his stumps. Lawrence showed his anger with himself by kicking furiously at the blameless crease.
However, the run-rate accelerated once Walter joined Pepper and the pair put on 36 inside four overs. Pepper hammered six fours and a six into the pavilion in a 20-ball knock before he leaned back and slashed Martin Andersson to backward point.
Walter, who had recorded single-figure scores in his previous two innings, was back to big-hitting form. The second of the quartet of sixes was the longest, clearing the scorers' box over de Caires's head. He perished when slicing Luke Hollman to cover point.
Sams slipped almost seamlessly into Walter's boots and battered 43 of the runs in a fifty partnership for the sixth wicket, in which Matt Critchley contributed three. However, Critchley still hit three sixes in an 18-ball 36 before he was caught by Joe Cracknell sliding in from the midwicket boundary. The pair had shared a stand of 79 in six overs.
Sams's eyes lit up in the final over in which Andersson conceded 26 runs, including three sixes, two off the last two balls, the first over fine leg, the second over third man.
The ubiquitous Sams was back on the scorecard when he held a pull from Stevie Eskinazi on the boundary to give Aaron Beard a wicket as Middlesex got off to a steady start in reply. He was in the same position to take the catch that ended Max Holden's whirlwind 15 off five balls during which 32 runs were compiled from just nine balls in partnership with Higgins.
Before that, Cracknell was dropped by Rossington on four and added six, four and a six in his 36 before misreading Critchley and seeing his bails dislodged.
Higgins reached his fifty from 20 balls with his third six, swept off Walter, but eventually fell when he pulled Critchley straight into Beard's hands on the midwicket fence.
The third and fourth wickets, with Higgins at the helm, accumulated 78 runs off 24 balls. But three wickets in seven balls turned the tide back in Essex's favour as Middlesex slide from 173 for 4 to 175 for 7. Sams tempted John Simpson in pick out short midwicket and Critchley had Hollman caught by Beard at mid-on and Alex Davies leg before.
Middlesex needed nine off the last over with two wickets standing but a six by Andersson off Walter's third ball all but wrapped it up.