Kisner - the runner-up to Bubba Watson at Austin Country Club 12 months ago - won the 18th hole to defeat Molinari and to book a final match-up against fellow American Matt Kuchar, who won this event in 2013.
Kuchar was also a 1up victor over Lucas Bjerregaard, the Dane who produced a stunning finish to eliminate Tiger Woods in the quarter-finals.
None of the first five holes in the contest between Kisner and Molinari were halved and the Open champion - who won all five of his matches at the 2018 Ryder Cup - won the seventh to get back on level terms.
Bogeys from Molinari at the 12th and 14th looked set to leave the Italian with too much to do down the stretch, but he birdied the 16th and 17th to get back to all-square.
However, having worked so hard to reach the 18th, Molinari three-putted the final hole, meaning a par was enough to put Kisner through to the final.
Kuchar was never behind against Bjerregaard, but the veteran was also unable to open up anything more than a 1up lead in another tense encounter.
Bjerregaard got back to all-square on four occasions and matched his opponent’s birdie at the 17th to send the match down the last.
Yet Kuchar was not to be denied as both men parred the 18th.
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