Kent needed just four runs off the last two balls with the big-hitting Justin Kemp, previously dropped by Middlesex stand-in captain Ed Joyce, facing.
But seamer Henderson sent down two dot balls to his fellow South African and ran his compatriot out off the last to seal a thrilling victory under the floodlights as Middlesex won their first major trophy for 15 years.
England batsman Owais Shah top-scored with 75 in Middlesex's total of 187 for six from their 20 overs before defending champions Kent, despite 49 from Kemp and 52 from captain Robert Key, the former England international, finished on 184 for five.
By reaching the final, Middlesex and Kent qualified for the Champions League due to be held in India later this year, where the winners will take home 2.5 million pounds (five million dollars) although that event is threatened by a dispute over the involvement of players from the rebel Indian Cricket League.
But winning the showpiece match gained Middlesex the lucrative additional prize of a place in the Super Series - the latest creation of American billionaire Allen Stanford - where they will be up against the England national side, a Caribbean All-Stars team and Trinidad and Tobago.
Kent started the last over needing 16 for victory.
Middlesex looked to have thrown away their chances of victory when an all-run four created by overthrows from Dawid Malan left Kent needing six off three balls. But Henderson kept his cool when all round him were losing theirs.
"It's been a very interesting day to say the least," said the 33-year-old Henderson, who earlier in the day starred with the bat by making a rapid 59 in Middlesex's eight-wicket semi-final win over Durham.
Middlesex off-spinner Shaun Udal, back on his old home ground, added: "I'd have preferred it not to have gone to the last ball. We were second favourites with a couple of balls to go.
"We're absolutely elated," the former England off-spinner, who took an impressive one for 21 in his maximum four overs in the final, added. "I thought these days were gone but they're back and I'm really pleased."
Earlier, Kent had beaten Essex by 14 runs in the semi-finals.
Middlesex 187/6 in 20 (Owais Shah 75, Tyron Henderson 43, Ed Joyce 23, Eion Morgan 23; Yasir Arafat 2/20, Ryan McLaren 2/36) beat Kent 184/5 in 20 (Robert Key 52, Justin Kemp 49, Darren Stevens 33, Joe Denley 31; Shaun Udal 1/21, Murali Kartik 1/30, Nannes 1/37).