Kent 231 for 5 (Billings 57*, Blake 42) beat Somerset 226 for 5 (Hildreth 45, Davies 45, Gregory 44*) by five runs
Scorecard
Kent Spitfires downed South Group leaders Somerset by five runs in a high-scoring thriller at Canterbury to book their place in the last eight of this year's Vitality Blast T20.
Kent's seventh south group win inflicted Somerset's fourth defeat in their final game of the campaign and extended the West Country county's woeful, winless T20 run against Kent to 11 matches dating back to 2011.
Batting first, Kent posted their highest short-form score against Somerset and equalled their best ever T20 total, matching their 231 for 7 scored against Surrey at The Oval in 2015.
Somerset chased manfully throughout, and needed a six off the last ball to tie only for Mitch Claydon to send down a near perfect yorker to seal the triumph.
Kent captain Sam Billings led the run spree with an unbeaten 57 from 35 balls, but Sean Dickson's cameo 20 from nine balls and a belligerent 42 from 22 deliveries by Alex Blake after a sloppy display in the field by the south group leaders.
With their place in the last eight already assured, Somerset elected to bowl after winning the toss, but Jerome Taylor's second over conceded a brace of boundaries to Daniel Bell-Drummond and 14 in total.
Joe Denly, Kent's leading T20 run-getter, plundered a straight six in Jamie Overton's first over that ended with a deft late cut for four, as the hosts, aided by six Somerset wides within five overs, raced to 50 after only 4.3 overs.
Taylor had Denly caught at short third man for 26 from the penultimate delivery of the powerplay to make it 67 for one then, with 37 off 21 balls to his name, Bell-Drummond pushed inside the line of a Max Waller legspinner that clipped off stump.
Waller and Roelof van der Merwe, the slow left-armer, stemmed the flow of Spitfires' boundaries until Heino Kuhn broke the stranglehold with a reverse sweep for six against Johann Myburgh as Kent reached the mid-point on 99 for 2.
Kuhn perished attempting to repeat the shot against a Waller full toss, picking out Corey Anderson at point, but Blake opened his boundary account with a straight six off Waller and greeted Overton's return with another maximum into the retirement complex adjacent to the ground.
Waller finished his stint with 2 for 29 as Kent reached 150 in their 16th over with Blake and Billings posting a 50 stand in 4.4 overs.
Billings unfurled his ramps, paddles and pulls to collect three successive boundaries in a Taylor over that cost 25 in total, but the partnership ended for 82 when Blake was superbly caught overhead by Overton at long-off for 42.
Kent's skipper reached his third 50 of the campaign from 31 balls, Taylor was taken out of the attack for his second beamer and the visitors conceded six penalty runs for failing to bowl their overs in the alloted time.
Chasing 232 at 11.55 an over, Somerset lost Myburgh after 15 balls to a stunning over-the-shoulder catch by Imran Qayyum that gave T20 debutant Grant Stewart his maiden wicket.
Steve Davies and Peter Trego, the former Kent allrounder, clattered a quickfire 59 in five overs before Trego holed out to deep square leg then Davies blotted his copybook by chipping Qayyum's second ball of the night straight to extra cover.
Qayyum conceded a huge leg-side six to James Hildreth as Somerset reached 102 for 3after 10 overs but, with the required rate rising to almost 13, Corey Anderson heaved against Calum Haggett to see Billings cling onto a skier running back towards third man.
With 82 needed from 30 balls, James Hildreth hooked a Mitch Claydon bouncer to long leg and despite late clubbing from Gregory and Tom Abell Somerset just fell short.
