Jacobson, a 36-year-old Swede who joined the tour eight years ago and has three European Tour victories, had just one bogey in the tournament and finished at 20-under, two shots off the course record.
"I was hitting so many fairways," said Jacobson, 14th last week in the U.S. Open at Congressional. "It started clicking the end of last week. The last two days I struck the ball the best I ever have at the U.S. Open."
Jacobson hit all 28 fairways over the weekend.
Rollins and Moore closed with 63s. Moore missed a 4-foot par putt on 18.
"I'm not beating myself up over that putt," he said. "That happens in golf."
Nineteen-year-old Patrick Cantlay, the UCLA star who had a 60 on Friday to break the tour record for an amateur, – finished at 11 under after weekend rounds of 72 and 70.
He arrived to a loud ovation on the 18th green, but bogeyed the hole.
"I just learned what it's like to have a week on the PGA Tour, to make the cut and to compete with all the guys," said Cantlay, the low amateur at Congressional last week. "This was just my second go-around and it was a lot of fun. The ovations are special every time."
Michael Thompson, who came out of qualifying school this season, shot the best round of the day, a 62, including a 29 on the back nine. He finished fourth at 18 under.
"It was very exciting, especially this being my dream to play on the PGA Tour," he said.
Jacobson was trying to become the first player since Lee Trevino in the 1974 Greater New Orleans Open to play 72 holes without a bogey.
And he almost did it.
He had 63 consecutive bogey-free holes before running into problems on the par-4 10th. His second shot went right, ending up resting against the cart path, but after taking relief and pitching onto the green, he couldn't make a 12-foot putt for par.
"I caught a mud ball there on the right side," he said. "You've just got to accept those. With a long iron, it can take off sideways so I got challenged there. But I think I dealt with it nicely and kept playing well."
Moore birdied his first three holes, making short putts on each and was 5 under for the day through the first seven holes.
He hit his second shot on the par-5 13th about 262 yards to 10 feet of the pin, but missed his eagle putt. His birdie put him in a three-way tie for the lead.
Moore made three more birdies in a row at Nos. 14-16 to got to 20 under and catch Jacobson again.
Moore hit into two sand traps on 18, but put a pitch inside 5 feet.
Jacobson's second shot stopped up about 14 feet from the hole, leaving him with an easy two-putt for the win.
After tapping in, he threw both arms in the air as his caddie slipped the flag off the pin as a souvenir.