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McDowell, who had rallied from four down to beat Gary Woodland in the first round, was forced to show his fighting qualities once again against Hideki Matsuyama.
The Northern Irishman was two down after 14 holes but he hit back to finish one-up after a parred the 18th at Dove Mountain.
"Why do it the easy way when the hard way will do?" McDowell said.
"I just got off to a slow start again, probably less so today. Hideki opened up three-three, so I was two down walking off the second green.
"I was quite proud of myself when I got a half on three, so I was only two down after three, as opposed to three down. But I made a bad swing on six, hit it in the right bunker there."
Having been three down after six holes, McDowell registered five birdies over the remaining 12 holes - with two crucially coming at the 15th and 17th.
"I played really clean golf," McDowell said. "I tried to go out there today and execute my game plan and try not to give him any room, try not to make any mistakes.
Massive putt
"And he kind of played the same kind of golf back. He played very, very well. I made big putts on 15 and 16, especially on 16, that was a massive putt to give me the opportunity.
"I feel very fortunate again today. I've certainly expended all my energy and emotions the last couple of days. But thankfully it's early in the season and I've plenty left in the tank."
McDowell's reward is a mouth-watering clash with Hunter Mahan - with 34-year-old having beaten the American in the decisive singles match to clinch the 2010 Ryder Cup for Europe.
"There's a decent chance he might be out for a shade of revenge tomorrow, who knows?" added McDowell. "It's been a long time, a lot of water under the bridge since 2010.
"He's a quality player. He's got a great record around this golf course and he's going to be a tough nut to crack.
"But I certainly feel I've had a pretty good workout the last couple of days, and I should be in good shape going into tomorrow."
