A near 6,000 crowd was silenced as the Red Rose county clinched victory with eight balls to spare courtesy of an unbroken fifth-wicket stand of 50 between Vilas and Jordan Clark.
The 2015 champions chased down the Spitfires’ inadequate 133-9 to beat the south group runners-up to qualify for next month’s finals day in Birmingham.
The Lightning also beat Kent at this stage three years ago, when they went on win the competition for the only time.
Needing to score at a seemingly comfortable rate of 6.7 an over for victory, Lancashire suffered the first-over shock of losing Jos Buttler to a golden duck, stumped by counterpart Sam Billings when pushing at a Joe Denly leg-spinner.
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Arron Lilley lost middle stump when looking to cut Adam Milne and Alex Davies might have gone for six had Imran Qayyum held on to a stinging caught-and-bowled chance as Lancashire ended their powerplay on 38-2.
Little and large third-wicket partners Davies and Jennings steadied the Lancashire ship with a stand of 44 before Davies holed out naively to long-off against Qayyum as the visitors went 7.3 overs without a boundary.
Jennings, the only batsman to time his drives, was four short of the game’s first 50 when he went to an athletic leg-side stumping by Billings as Qayyum finished his excellent stint with 2-17.
With 23 required off the last 18 balls, Vilas (30not out) and Jordan Clark (29n.o.) held their nerve with a half-century stand in 5.3 overs, which included Lancashire’s only six from Clark. Batting first after winning the toss, Kent’s top-order struggled for timing on a dry pitch as Lancashire skipper Vilas intelligently took pace off the ball by utilising four spin bowlers.
The hosts took 11 runs from the first over by off-spinner Steven Croft but crucially lost opening bat Daniel Bell-Drummond run out without facing off the second ball of the night.
Denly worked the ball to square leg and set off but Bell-Drummond hesitated and lost the race, despite a sloppy throw by Keaton Jennings.
Heino Kuhn followed in the next over from Poulton’s Toby Lester, nicking through to keeper Buttler.
Buttler took his second catch when Spitfires’ leading T20 scorer Denly, with only 13 to his name, edged Clark.
Spitfires limped to the end of their powerplay on 40 -3 and should have lost Sean Dickson with the total on 43 only for Buttler to fumble a stumping chance in the first over of left-arm spin from Zahir Khan.
Kent, who last reached finals day in 2008, eventually raised 50 in the eighth over but, with spin from both ends, boundaries were elusive.
Billings and Dickson added 40 before Dickson, trying to force the pace, skied one from leg-spinner Matt Parkinson to deep extra cover.
Man of the match Parkinson struck again four balls later, having Marcus Stoinis caught at slip for a third-ball duck to make it 63-5 at the mid-point of Kent’s innings.
Alex Blake gifted Parkinson the last of his 3-27 return when holing out to deep mid-wicket.
Then top-scorer Billings missed his late cut against Zahir to lose off stump afte a run-a-ball 37.
James Faulkner snared Milne leg and in the next over pocketed a comfortable catch after Calum Haggett ballooned to mid-wicket.
Kent’s No10 Qayyum chipped and chased to become their second-top-scorer with an unbeaten 21 but it was a total well within Lancashire’s compass.
Vilas said: “I thought we bowled incredibly well and we were happy to keep them to that score, though obviously we didn’t expect the pitch to turn that much.
“Keaton came in and got a few away, rotated the strike well and made sure he took us deep.
“We expected the pitch to grease up a bit and skid on under lights but credit to Kent – they worked hard in the field and bowled really well.
“I’ve got bruises and scars all over my body from diving around trying to turn ones into twos and I’m delighted we made it over the line.”
Kent captain Billings said: “We needed to get a couple of their big players out at the top but Dane played brilliantly and Keaton as well.
“Considering the tough week he’s had with England, to come here under pressure and play that well I thought was a top knock.”