'It feels pretty good,' said Ogilvy of his first win. 'I didn't know how it was going to feel. It feels pretty nice.'
Na and Ogilvy were in the final group together. Ogilvy was at 20 under, but bogeyed the 15th to slip back to 19 under. He parred his final three holes to post a final-round 71.
Na, meanwhile, bogeyed the 15th to drop back to 18 under. He closed with a birdie at the last to finish a round of 1-under 71 and force a three-way playoff at Omni Tucson National Golf Resort and Spa.
In the playoff, Calcavecchia made a mess of the first extra hole, No. 18. He flew over the green and into a bunker with his second, then left his bunker shot in the sand. He pitched out with his fourth and two-putted for double bogey.
Na missed the green to the right, but got up and down for par as he drained a 27-foot par-saving putt. Ogilvy was standing on the green the whole time looking at a 28-foot birdie putt.
He missed his birdie try and after kicking in his par putt, it was off to the 10th along with Na.
Both players found the right rough off the tee. Ogilvy pitched out from his poor lie, while Na played an excellent shot to the back edge of the green with his second.
Ogilvy dropped his third 18 feet from the cup. Na rolled his chip 8 feet by the hole. Ogilvy stepped up and sank his birdie putt. He then watched as Na missed his 8-footer for birdie, giving Ogilvy his first PGA Tour title.
'In that situation, it's a bit like match play. You have got to tell yourself the guy is going to make it,' said Ogilvy, who picked up $540,000 for the win. 'It was hole it or go home in my head. I found a way to hit a good putt and it went in.'
Steve Stricker took fourth place at 18-under-par 270 after a final-round 68. Doug Barron finished one stroke further back at minus-17.
Aaron Baddeley (68), Brent Geiberger (71) and Billy Mayfair (70) shared sixth place at 16-under-par 272.
Ogilvy, who shared the third-round lead with Na, fell one behind Na when the Korean birdied the second. Ogilvy came back with a birdie at the third and when Calcavecchia birdied the fifth, there was a three-way tie for the lead at 19 under.
Calcavecchia briefly took a one-stroke lead when he drained a birdie putt at the sixth. However, Ogilvy tied Calcavecchia with a birdie of his own at the fifth. The Australian then took the lead with a birdie at the sixth.
Calcavecchia fell two off the pace with a bogey at the ninth, but bounced right back with a birdie at No. 10. When Ogilvy bogeyed the 11th, the two were tied for the lead.
Calcavecchia bogeyed 13 to drop to 19 under. Ogilvy later bogeyed the 15th to tie Calcavecchia in the lead. Na, who also bogeyed the 15th, bounced back with a birdie at 18 to forge into the three-way playoff.
'The way I play golf these days, I'm not going to be in that kind of position that many times,' Calcavecchia said. 'My game has deteriorated a little bit. It's hard to have a chance to win in the my state of the way my game is and my age and the way my body feels. So it's tough to lose.'
'To me, it's just a matter of time when I'm going to win,' said Na, who is the youngest player on tour. 'And I feel like I have grown as a player, becoming a better player.'