Trailing by three strokes with four holes to play, Baddeley made three consecutive birdies from No. 15 and walked away with his second career PGA TOUR victory.
He shot his second straight 7-under 64 for the lowest weekend score in tournament history.
He hit an ill-advised driver into the water at the 332-yard, par-4 17th, then chipped within 4 feet before missing the short putt and settling for bogey.
Baddeley, meanwhile, made a 10-footer for birdie and pulled ahead by one shot. He closed with a routine par at the 18th to finish at 21-under-par 263.
Quinney hit two bunkers and made another bogey at the 18th to close out a 3-under 68. He finished one shot behind John Rollins, who slipped into second place at 20-under 264 after quietly shooting the round of the day with an 8-under 63.
It was a bizarre ending involving two players who live in the same nearby community.
'I'm sure Jeff is disappointed about how he finished. But I was really just trying to put pressure on him towards the end,' said Baddeley, who won $1.08 million.
'When I got three back I was really just thinking if I can be one back playing the last hole, I've got a chance. I just tried to make some birdies, and that's what I did.'
Baddeley claimed his first PGA TOUR win at last year's Verizon Heritage.
'I was definitely a lot more calm today than I was at Hilton Head coming down the stretch,' he said. 'I had a lot more confidence, probably because I had been there, but also because I was more comfortable in my golf swing.'
Quinney will make the short trip home knowing that he probably let win No. 1 slip away. Although Sunday marked his third consecutive top-10 finish this season, he stopped short of admitting failure.
'I was sleeping on the lead the last couple days and it was a lot of pressure and I'm happy how I handled the whole situation,' Quinney said.
His late collapse cost him $672,000 -- the difference between first and third place. His closing bogey at the 18th was also expensive: He ended with a $408,000 check, while Rollins walked away with $648,000.
Quinney may replay his decision to hit driver off the tee at the reachable 17th instead of playing it safe with a 3-wood. He was adamant that he needed to make a birdie 'because I knew basically they were going to make birdie.'
'I was shocked to see it go left,' Quinney said. 'I was really confident I was just going to knock it on the middle of the green. It was one those things -- you look up and it's going left.'
Then, the missed 4-footer for par.
'I hit a great recovery shot. It was a tough pin back there, and I didn't execute. But I'm not going to dwell on that,' Quinney said.
He would have had less to think about if Baddeley hadn't made his birdie putt.
'I assumed he was going to make par, so I knew I still had to make my birdie to either pull even or just put pressure on him,' Baddeley said. 'That was probably one of the best putts I hit all week there.'
Baddeley trailed by three shots after 10 holes but momentarily caught Quinney with a birdie at the 13th. Quinney answered right back with a birdie to remain one ahead.
Busy fending off challenges from Rollins and Bart Bryant as well, Quinney made a 6-foot birdie putt at No. 14 to move two ahead.
'I played pretty dang good golf today,' he said.
But Baddeley began making his run with a two-putt birdie at the 15th. At the par-3 16th -- in front of the raucous TPC of Scottsdale stadium gallery -- he knocked a wedge within 24 feet to set up another birdie.
Quinney, a former player at Arizona State, was 26 feet away but couldn't capitalize.
'If I didn't win, I guess I'm glad a local guy won,' Quinney said. 'I just hope to be back in the hunt quickly. I just want to get back there again, and I know my time will come soon.'
Rollins may have forced a playoff if he hadn't gotten unlucky at the 18th. His approach shot was dead-on, but it hit the flag stick and rolled back off the front of the green. He made par.
'I got a bad break, but it is what it is. I played solid,' said Rollins.
Bryant had two late birdies and shot a 66 to finish in fourth place at 18-under 266. Billy Mayfair (65) was at 267, Heath Slocum (66) shot 268 and Vijay Singh (64) was a stroke further back at 269.