Koepka started the day four shots behind Kevin Chappell, and birdied five of his first eight holes to charge up the leaderboard. He set the clubhouse lead after a birdie on No. 18 closed out a 7-under 65, but could only watch from the range as Chappell rolled in a birdie of his own to finish one shot ahead.
Koepka earned his first win at the 2015 Waste Management Phoenix Open and has had several close calls since, including a playoff loss to Sergio Garcia last year at the AT&T Byron Nelson. After a slow start to the year, he now has three straight finishes of T-11 or better and believes his game is on the rise as the summer approaches.
"I'm playing really well. It's hard to win out here. I think everybody knows that," Koepka told reporters. "Feel like I'm really knocking on the door of getting the second win, and hopefully it comes soon."
Koepka was left to rue a short birdie miss on No. 14, as well as a second-round 74 that left him with plenty of ground to make up. But despite the close call, he's eager to turn the page to next week's Zurich Classic of New Orleans where he will team with his brother, Chase, who will be making his PGA Tour debut.
"It will be fun. I don't get to see my brother play too much," Koepka said. "I'm playing well, he's playing well. He's actually done pretty well in some tournaments lately. It will be fun but it could be interesting, the little brotherly love we could kill each other on the second hole, or it could be awesome."