American Kisner, 33, trailed overnight leader Webb Simpson by three strokes before clinching the second PGA Tour title of his career.
Defending champion Jordan Spieth, 23, was tied second with fellow American Sean O'Hair and Spain's Jon Rahm, while Simpson finished fifth in Texas.
England's Paul Casey started the day tied second but ended tied in 10th.
The 39-year-old recorded four bogeys in a torrid final round.
Simpson, who had a two-stroke lead going into the final round, bogeyed the first and last holes.
Rahm, 22, had the best chance to force a play-off, but missed a 10-foot birdie putt at the last as Kisner overcame late nerves to secure victory.
He had a bogey at the 16th before sinking a five-foot par-saving putt at the final hole.
"I'm just happy to win any tournament, but especially here. I love this place," said Kisner.
Kevin Kisner produced six birdies in a final round four-under-par 66 to win the Dean & Deluca Invitational.