Morland closed a bogey-free round with a birdie on the 18th to get into the clubhouse at 8-under-par 280 after a final-round 68. Thompson carded back-to-back birdies from the 17th to shoot 68 himself and force the playoff.
On the first extra hole, Thompson two-putted par to down Morland, who tripped to a bogey as he could not save par from a greenside bunker.
'It feels wonderful. I wasn't nervous at all today,' admitted Thompson. 'I was swinging good and I played so well on the last 11 holes. I had a look for birdie on every one of them.'
Thompson entered the final round at Clearwater Resort two strokes behind third-round leader Ryan Howison. Thompson slipped further back with a bogey on the par-4 third.
The 24-year-old recovered that lost stroke with a birdie on the par-4 eighth. Thompson moved into contention thanks to back-to-back birdies from the 10th.
Thompson parred his next five holes to remain at 6 under. He birdied each of the final two holes, including the 18th from 4 feet out, to tie Morland and force the extra session.
'For nerves, you couldn't have had two better putts,' said Thompson of his 6- and 4-foot birdie putts on 17 and 18. 'They were both up the hill and inside the hole. You put a good stroke on it and you can't miss.'
Morland got going with five straight pars. He birdied the sixth and eighth to climb to minus-6.
The 37-year-old Morland again ran off five straight pars. He moved into a share of the lead at minus-7 with a birdie at 14. Morland grabbed the lead by himself for the first time with a birdie on 17 before he was caught by Thompson.
Michael Letzig, who held a share of the lead after round two, closed with a 7-under 65 to end in a tie for third at 7-under-par 281. He ended alongside Lee Williamson (69). James Nitties was one stroke further back at minus-6 after a closing 71.
Mark Brown, Jason Day, Howison and Sal Spallone tied for sixth place at 5-under-par 283.