The hard-throwing left-hander made it look as easy as 1-2-3.
Chapman struck out two in a perfect ninth to finish a one-hitter in the Yankees' 3-1 win over the Texas Rangers on Saturday.
Tyler Austin hit a go-ahead single in the ninth inning for the wild card-leading Yankees.
"I feel good about him out there," manager Joe Girardi said. "This is a guy that's been too good for too long, for me, to lose it. It's good to get him back out there. He threw well."
Before the game, Girardi said he would prefer to settle on a closer over the committee approach he has employed since demoting Chapman after he gave up two runs in a non-save situation in a 9-6 loss at Boston on Aug. 18.
Chapman had his fifth scoreless outing in six appearances since, capping it with a swinging strikeout of pinch-hitter Mike Napoli on a 102 mph fastball for his team-leading 17th save in 21 chances.
"Really nice," said starter Luis Severino, who struck out 10 in seven innings in his first no-decision since July 15 at Boston. "I know he can throw a strike. I know he can get that role, that save."
The only hit off Severino was Brett Nicholas' run-scoring double with two outs in the fifth. Will Middlebrooks, the lone runner past second against Severino, scored from first.
David Robertson (7-2) pitched a perfect eighth.
Chase Headley drove in two runs without a hit — a tying sacrifice fly in the eighth and a bases-loaded walk for a 3-1 lead in the ninth.
Alex Claudio gave up a single to pinch-hitter Matt Holliday, putting Frazier at third with no outs and setting up Headley's sacrifice fly an out later.
"I felt like I could have kept going, but I thought Frazier was going to come out swinging," Cashner said. "I wasn't trying to throw a strike and it just sailed on me."
Claudio (4-2) allowed four singles among eight batters he faced. Frazier was hit by a pitch again in the ninth by Ricky Rodriguez, who allowed Austin's go-ahead hit and Headley's walk.
Severino struck out 10 or more for the fifth time this season, the first since July 8 against Milwaukee. The 23-year-old right-hander is the first Yankees pitcher to allow one or no hits in at least seven innings since Michael Pineda against Baltimore on Sept. 22, 2014. "He was really good today," Girardi said. "It looked like he had great command of his fastball."
Another Gomez Injury
Texas center fielder Carlos Gomez left after rolling his right ankle on a swing in the second inning. He didn't even make it halfway to first on the groundout and needed help getting off the field. He was on crutches with a walking boot after the game. Gomez missed a month in May and June with a hamstring strain and was on the 10-day disabled list last month to have a cyst removed behind his right shoulder.
It was the fewest hits for the Rangers since opening day last season, when they beat Seattle 3-2 despite getting just one hit. ... Aaron Judge walked in the second inning to tie the major league rookie record of 106 by Cleveland's Les Fleming in 1942. ... Cashner's no-decision was the sixth time this season a Texas starter went at least seven innings allowing one or no runs without getting a win. ... The Yankees won for the eighth time this year when trailing after seven innings.
Yankees: Rookie LHP Jordan Montgomery (7-7, 4.14 ERA) will make his 26th start on an extra day of rest. He hasn't won since July 25 against Cincinnati, a span of six starts.
Rangers: RHP A.J. Griffin (6-5, 5.09) pitches on seven days' rest. He is 3-0 in five starts against the Yankees.