After making a bogey on the 17th at Waialae Country Club, PGA Tour rookie Baddeley birdied the 18th to force extra holes.
Els and Baddeley, who both finished 72 holes on 264 (16 under par), birdied the 18th in the playoff, then moved to the 10th where the world number two clinched victory over his 21-year-old rival to win his second successive PGA Tour title.
Chris DiMarco was third on 266 while defending champion Jerry Kelly and Australian Robert Allenby tied for fourth. Stuart Appleby, another Australian, was alone in sixth place on 269.
The victory was worth $810,000 to Els, who last Sunday pocketed $1 million for winning the Mercedes Championship title.
Both players made birdie putts of seven feet at the first extra hole before moving to the 10th, a 353-yard par four playing downwind.
Els, who had driven the hole earlier in the day, missed the green left while Baddeley hit his tee shot into the same greenside bunker that he had visited in regulation.
The South African hit a chip that went across the green and rested on the fringe, 55 feet from the hole. Baddeley played an indifferent sand shot and faced an uphill 20-footer.
STAY ALIVE
But Els struck a putt that never wavered on its path to the hole. "I was just trying to stay alive
"It's crazy, I was trying to make it but from 55 feet what are your chances really?. So, you hit the best putt you can and hope for the best."
Baddeley's putt was on line but stopped agonisingly on the edge of the hole.
"I didn't think he was supposed to hole that putt," said the Australian. "I wasn't expecting him to anyway.
"That was a heck of a putt he made."
"I really felt I was swinging well today," said Els, who began the day two strokes adrift of overnight leader Baddeley.
"I could see Aaron wasn't comfortable with his swing but he is young, he's full of confidence. He's got so much talent, he just stuck in there and he never let go."
Els drew level with Baddeley by the turn before driving the par-four 10th to make a birdie and snatch the lead.
Baddeley made a birdie at the 14th but gave it back by three-putting the 17th when a door slamming on a portable toilet distracted him and he had to step away from his par effort.
One down with the par-five 18th left, Baddeley watched as Els missed his 12-foot birdie putt. The Australian then stepped up to drain an 11-footer for birdie.
"It was a tough day today, I didn't strike it the best," Baddeley said. "I didn't drive it very well but I hung in there.
"I just stuck it out, grinding, making pars and trying to stick with Ernie."
