Koepka, a member of the U.S. Ryder Cup team previous year, was looking for his second PGA Tour win.
He made a clutch par save at 17 after he drove to the front fringe and opted to putt, but he misjudged the line and pace and then raced his birdie putt four feet past the cup before the return dropped in the left side.
Chappell consistently failed to slam the door with several two-putts over the back nine.
Koepka, who entered the tournament ranked 24th in the world, had five straight pars before a birdie on 18 to tie Chappell for the lead at 11 under.
"I'm just excited that I don't have to answer that question of, 'What do I have to do to win?' again". He tapped in to gain a stroke, and he made good two holes later with a 12-foot birdie. The most notable of that group was Koepka, who posted the clubhouse lead after a closing 65, but Chappell's birdie on the final hole gave him the winning margin and led to an epic post-victory celebration.
Brendan Grace (73), the first-round leader, finished at 282 along with Camilo Villegas of Columbia (70) and second-round co-leader Bud Cauley (72).
Giraffe cam with April, baby to end on Friday
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Kevin Chappell of the U.S. hits off the second tee in first round play during the 2017 Masters golf tournament at Augusta National Golf Club in Augusta, Georgia, U.S., April 6, 2017.
Round of the day: Koepka started the day four shots off the pace, but he made a quick move up the standings with five birdies over his first eight holes. He putted from 13 feet to save bogey.
CHAMPIONS TOUR: Carlos Franco and Vijay Singh teamed to shoot a course-record 12-under par and rally from seven shots behind to win the Bass Pro Shops Legends of Golf in Ridgedale, Missouri.
At Shenzhen, China, Austrian Bernd Wiesberger beat England's Tommy Fleetwood in a playoff on Sunday to win the Shenzhen International. The 40-year-old said the results are great for his confidence heading into the middle of the PGA Tour season. Wiesberger went into the final round with a three-shot lead and eight shots ahead of Fleetwood but the Englishman fired a 63 to finish tied at 16 under.
He birdied three of his last five holes. His 8-foot birdie putt on 18 finally sealed it with a final round of 68.