Bae missed a short birdie putt on the 18th that only affected the margin. He closed with a 1-over 73, the first player on the PGA Tour since Ben Crane at the St. Jude Classic in June to win with a final round over par.
He won by two shots over Steven Bowditch, who closed with a 67 on a dry, hot day in the Napa Valley.
The only drama came from the 28-year-old South Korean, who was six shots ahead when he made a par on the 10th hole. Bae had a trio of three-putts - two of them from just off the green - to start coming back to the field.
But no one got closer than two shots all day.
Hunter Mahan, one of four players in the field who were in the Ryder Cup two weeks ago, looked as if he might make a run when he holed out from 91 yards on the 13th hole for eagle to get within two shots of the lead. But he hit a poor chip on the 15th that led to bogey, and he barely got out of the bunker on the par-5 16th, which kept him from a birdie.
Mahan closed with a 70 and wound up in five-way tie for third with Retief Goosen, Hideki Matsuyama, Martin Laird and Bryce Molder. Matsuyama finished with two straight birdies, and tied for third for the second straight year at the Frys.com Open.
Zach Blair, the PGA Tour rookie who played in the final group, was out of the mix quickly with early bogeys. He had a 74 to tie for 12th, five strokes back.
Bae, who finished at 15-under 273, won for the second time in his career and earned a return trip to the Masters in April.
He looked shaky, even when no one was making a run at him. Bowditch birdied the 18th to reach 13-under 275, and he even went to the practice range as Bae kept missing greens and scrambling for par.
Bae took three putts for bogeys on the 11th, 13th and 14th holes, though a 15-foot birdie putt on the 12th steadied him briefly. If there was a key shot, it might have been on the par-5 16th. He drove into a nasty lie in the rough, gouged it out to the fairway, and then aggressively went at the back pin with a sand wedge. It took one hop on the firm greens and wound up in the rough.
The chip came out clean and rolled to 2 feet for par and slight relief. He again went just over the back on the 17th, and hit another safe chip to tap-in range that kept his lead at two shots playing the par-5 18th.
''I think I was a little nervous,'' Bae said. ''This course wasn't easy, actually. I'm very, very happy.''
Matt Kuchar, playing in the penultimate group and starting the final round five shots behind, fell back quickly by missing a 4-foot putt on the opening hole and hitting behind a tree on the third hole. He closed with a 76. Brooks Koepka missed several birdie chances late that could have at least made Bae think. He had a 72 and had to settle for a top 10 in the PGA Tour opener, along with Hudson Swafford, Jon Curran and Robert Allenby.
Lee Westwood had a 69-67 weekend and tied for 12th.
Jarrod Lyle, in his first PGA Tour start since a recurrence of leukemia some 18 months ago, shot par or better all four days and closed with a 70 to tie for 31st.
Goosen played with Bae the opening two rounds and knew what he was up against on Sunday.
''He hit the ball very well and his putter was super hot,'' Goosen said. ''I knew he was going to be tough to catch this weekend the way he was striking it. He's not really going to make many mistakes.''
Bae made his share, though by then it was too late to matter.