Montgomerie, the defending champion, closed with a 66, while Langer shot a 68 to finish in a tie for third with New Zealand’s Grant Waite.
“I had a lot of good runs in the U.S. Open over the years and probably lacked a little maturity to pull it off,” said Maggert, who had 13 top-10 finishes in majors in more than 20 years on the PGA Tour.
“But certainly, now that I'm an old guy, I've learned a lot and was able to just steady myself and play well.”
The final round started with 16 players within two shots of the lead and Maggert said he knew he had to build momentum.
“It was a little different, having so many guys close,” he added. “A lot of really good players that have been playing well.
"So I knew I couldn't go backwards today. I had to get a mindset to go forward and make birdies.”
After six birdies in 15 holes, he made his only bogey at No. 16.
Of the last eight senior majors, Maggert has now won two, while Montgomerie and Langer have won three each.
(Editing by Peter Rutherford)
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