Kirk went bogey-free as he overturned a two-shot deficit to finish 15 under after carding a five-under-par 66 at TPC Boston in Norton, Massachusetts.
The 29-year-old had five birdies throughout his 18 holes as he captured his third PGA Tour title.
Kirk is now top of the FedEx Cup rankings following his victory in the second play-off event.
Australian Geoff Ogilvy was two shots off the pace as he secured his spot in next week's BMW Championship.
Needing to finish inside the FedEx Cup top 70, Ogilvy shot a six-under-par 65 to avoid the 30-man cull, with the veteran projected to move into 24th position.
Overnight leader Russell Henley and Fellow American Billy Horschel were also 13 under through 72 holes.
Henley was well poised heading into the final day but he could only manage a 70, which included two bogeys.
Horschel posted a similar round after a bogey at the 18th hole seeing him finish with a 69.
Rory McIlroy was expected to surge to the summit but his charge never materialized as he ended the tournament four shots back at 11 under.
The world number one shot a 64 in the third round but a one-under-par 70 was all he could manage on Monday.
McIlroy, however, is second in the FedEx Cup standings ahead of the third play-off event in Cherry Hills Village, Colorado.
The Northern Irishman had company at 11 under with four birdies from eight holes helping Australian John Senden to a five-under-par 66.
Senden's top-five placing is expected to see him jump from 28th to 16th in the rankings.
German Martin Kaymer (67) finished in a share of seventh alongside Australian Jason Day.
Day - seventh in the rankings - was in the mix throughout the tournament but a bogey and double bogey on the back nine left the FedEx Cup hopeful five shots off the lead.
There was a seven-way tie for ninth, with Swede Carl Pettersson the pick of the bunch after his 66 on the final day sealed his place inside the top 70.
American Jimmy Walker (67), Robert Streb (68), Bill Haas (69), Chesson Hadley (69) and Webb Simpson (71), and South Korean Noh Seung-Yul (70) were also nine under.
Ninth was good enough for Hadley, who rose 27 spots from 84th to 57th.
Though it was not enough for Streb as the American narrowly missed out on a BMW Championship berth, finishing 71st.