Murray, An and Bradley replayed the par-5 18th at Waialae Country Club to begin the playoff on Sunday. Murray's drive hooked left and appeared to hit palm trees on its way down, but after he punched out into the fairway, he got on the green in three.
Bradley's second shot sailed into the grandstand and required a drop.
An appeared to be the most likely victor when he chipped his third shot from the greenside rough to within four feet of the cup.
But after Murray sank his long birdie try in the dead centre of the hole and Bradley missed a birdie, An's putt to extend the playoff trickled past the hole.
Murray shot a bogey-free, three-under 67 to force his way into the playoff at 17-under.
The 30-year-old stopped drinking alcohol last year in an effort to improve himself. He cited Chris Kirk as an inspiration after Kirk took time away from the tour to address mental health and addiction concerns.
Now, the 2024 PGA Tour season has begun with Kirk and Murray winning the two Hawaii-based events. Kirk captured The Sentry, the season opener, last week in Maui.
South Korea's An, who finished fourth at The Sentry last week, recovered from a bogey-birdie-bogey start to his final round by keeping a clean card the rest of the way.
He made a 15-foot eagle putt at the par-5 ninth and nearly had a similar result when playing the 18th in regulation.
An hit a 242-yard approach shot to 13 1/2 feet from the pin. He two-putted for birdie to move to 17 under and tie Bradley for the lead.
Murray and Bradley missed the fairway with their drives at No. 18 and both punched out. But Murray, who was one off the pace at the time, hit a tight third shot inside three feet and tapped in for birdie to join the leaders at 17 under.
Bradley also got on in three but missed a 23 1/2-foot birdie putt to win outright, leading to the playoff.
The trio finished ahead of Russell Henley and China's Carl Yuan, each of whom shot 63 to tie for fourth at 16-under 264.
Cam Davis was the leading Australian, shooting 69 to finish tied for 30th.
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