By finishing in the top eight, they will earn invitations to the Masters Tournament next spring.
The two tied for third and were low Americans at Congressional Country Club, earning their first trip to Augusta.
Garrigus made a lengthy putt to save par on the final hole, but he didn't realize he had a stroke to spare.
"That was one of the things I will never forget. Besides it being Father's Day and to have my son there afterwards and everything, this is a pretty special day," said Garrigus, who shot 4-under 32 on the final nine. "And to make that putt, I get into Augusta, that's probably one of the coolest things I'll ever get to say is I am playing at Augusta next year."
Chappell, meanwhile, played the final nine holes in 3-under.
"Being low American, that's great," Chappell said. "I don't think the state of American golf is where everyone expects it to be, but I think it shows that someone like myself can play out here, and I think it's definitely going to end up going in the right direction here sometime soon."
In addition to Garrigus and Chappell, others finishing in the top eight were McIlroy, Jason Day , Lee Westwood , Y.E. Yang , Peter Hanson and Sergio Garcia .
FAST FINISH: Reigning Masters champion Charl Schwartzel finished strong with 5-under 66 to tie for ninth.
Schwartzel played the front nine in 2-under, then nearly holed a pair of iron shots on the final nine. In his Masters win, the South African chipped in for birdie on the first hole of the final round and holed out for eagle on the third hole.
"I played pretty spectacular today actually," Schwartzel said. "The whole thing is everyone can always say I could have played better, but I had a really good low score. I made five birdies, no bogeys on a final day of a U.S. Open. I think I'm pretty happy with that."
Schwartzel nearly holed his tee shot on the par-3 10th. Then, on the par-4 17th, he nearly holed out with his 7-iron approach.
SPECIAL WEEK: Russell Henley doffed his cap and then waved to the crowd adjacent to the 18th green.
Then he turned and hugged his brother and caddie, Adam .
It was another special week for the University of Georgia golfer, who shot 4-over 75 to finish at 4-over 288.
"Coming down the 18th, the sides were just filled with people, and everybody stood up and clapped for me," Henley said. "It's something I'll remember for a long time. It was loud. Yeah, I hit some shots and had a decent tournament. But that was a beautiful moment."
Henley was trying to become the first player to win low amateur honors in consecutive years since Phil Mickelson in 1990-91, but he was edged out by Patrick Cantlay. The California amateur shot 1-over 72 and finished at even-par 284.