'I'm glad. I'd prepared for this event pretty well and I had always come close before,' said Singh, who earned $864,000 for the win. 'I just hung in there. I had a lot of chances at birdie on the back nine, but I didn't take advantage until the last one.'
Els made a dramatic eagle putt on the final hole to match the course record of 8-under 62 to come in at 10-under-par 270.
Shigeki Maruyama, who held the lead after rounds two and three, struggled to a final-round 71 to end the event at minus-9. He was joined in a tie for third place by Charles Howell III, who posted a 3-under 67 in the final round.
Singh opened the final round four strokes behind Maruyama. However, the Fijian stuck his second shot within 2 feet to setup birdie on the second at Waialae Country Club. Singh posted six straight pars before making his move.
The top player in the world birdied the par-5 ninth to get to minus-8. Singh came right back with an 18-foot birdie putt at the 10th to get within one of Maruyama and Robert Gamez, who posted a 3-under 32 on the front nine to grab a tie for the lead at minus-10.
Singh joined them atop the leaderboard as he rolled in a 10-foot birdie putt at the 11th. As Singh converted his par putt on the 12th, he heard the roar of the crowd from the 18th as Els drained a 16-foot eagle putt to jump to minus-10 to create a four-way tie for the lead.
Gamez fell off the pace as he bogeyed four straight holes on the back nine. Maruyama dropped shots at the 12th and 14th to drop behind Els and Singh.
Singh, who parred Nos. 12-17, shared the lead with Els as he stepped to the 18th tee. The reigning PGA Championship winner crushed his drive down the middle, carrying his drive over 310 yards in the air.
He left his second shot to the par-5 on the front fringe. Singh rolled his eagle try from 50 feet out just by the cup and tapped in for birdie to gain a one-shot cushion over Els, who had finished nine groups ahead of Singh.
'I was thinking about it coming down 16 or 17 that I hadn't birdied the 18th all week,' said Singh. 'That's a good opportunity for me to birdie, but I had to drive the ball well and I did. The putts didn't go in on the back nine, but I made one when it counted.'
Maruyama had a chance to tie Singh at the last. He needed to hole out for eagle from 92 yards out, but was unable to do it giving Singh his 25th PGA tour crown.
Els, the No. 3 player in the world, posted four birdies to go along with one bogey on the front nine to move to minus-5 for the event. After a birdie at the ninth, the South African made it three straight as he converted birdie attempts at 10 and 11.
He stumbled to a bogey on the 14th. Els made his charge with birdies at 16 and 17 to set up his dramatic eagle at the last.
'I played well today,' Els said. 'I threw a little three-putt in there, the bogey on 14, but other than that I played pretty good. It was fun and exciting, and especially the finish. Finishing birdie, birdie, eagle was really great. But I always felt I was going to be just a little shy, because you think the leader tees off at 10 under, you would think 12 under would be the number. But I still had a great day.'
Stewart Cink fired a 5-under 65 on Sunday to climb into a tie for fifth at 8-under-par 272. He was joined there by Brett Quigley, who closed with a 1-over 71. Tommy Armour III and Andrew Magee were one stroke further back at minus-7.
Gamez was unable to recover from his four back-nine bogies. He posted a 71 to end in a share of ninth place at 6-under-par 274. Gamez was tied there by Bart Bryant (69), Tom Lehman (69) and Craig Stadler (67).