Despite a good fight from Toronto's blossoming rookie hitters, the hard-throwing closer was up to the task.
Tanaka and Chapman combined on a four-hitter, Brett Gardner had an RBI double, and New York beat the Blue Jays 1-0 Sunday to end a two-game skid.
Tanaka (8-6) allowed three hits while pitching into the ninth inning, walking none and striking out four. The right-hander was pulled after Brandon Drury singled to begin the ninth.
"He was able, for the most part, to stay off the barrel all day long," Yankees manager Aaron Boone said.
Chapman came on to face pinch-hitter Vladimir Guerrero Jr., who fell behind 0-2, worked back to a full count, hit a foul ball off the fifth deck and finally grounded into a double play to end the 13-pitch encounter.
"That's obviously, in a lot of ways, the ball game there," Boone said. "In a very well-played, 1-0 game, you've got a young, rising, great-looking hitter against the game's dominant closer. It was a great match to watch those two guys go at it."
Guerrero fouled off seven pitches before grounding out.
"It was a great at-bat by him," Chapman said through a translator. "He made me work."
Some in the crowd of 27,790 rose for a standing ovation as Guerrero returned to the dugout.
"I've never seen somebody hit a double-play ball and get a standing ovation," Blue Jays manager Charlie Montoyo said.
Chapman gave up a single to Bo Bichette, then fanned Cavan Biggio to earn his AL-leading 31st save in 36 opportunities.
"That was some really quality at-bats going up against our guy there at the back end, who was dealing," Boone said. "I think there was probably a little more energy than normal, based on how that inning unfolded. It was a good way to finish off a trip after a couple of losses."
After the clubs combined for 37 runs and 13 homers over the first three games of the series, offense was at a premium in the finale. Toronto's stretch of 15 straight games with a home run ended, as did New York's nine-game streak of multihomer efforts. New York has scored at least a run in 200 consecutive games, the fourth longest streak in major league history.
Yankees All-Star Gleyber Torres returned and went 0 for 3 at shortstop after sitting out the past four games because of an unspecified core injury.
New York third baseman Gio Urshela bobbled Bichette's chopper to third to begin the game but the Blue Jays rookie shortstop was credited with a base hit, snapping an 0-for-8 stretch.
Justin Smoak reached on DJ LeMahieu's fielding error in the second but the Blue Jays didn't have another baserunner until Smoak singled through the shift to begin the eighth. The hit ended a run of 17 consecutive outs.
Urshela made up for his earlier miscue with a leaping catch on Randal Grichuk's hard liner in the fourth. Fully extended, Urshela dived toward the line to make the play and end the inning.
Blue Jays right-hander Trent Thornton was perfect through four innings before Urshela doubled to begin the fifth. Urshela's hit dropped in front of a sliding Teoscar Hernandez, who initially broke back. Gardner followed with a ground-rule double.
New York loaded the bases with one out in the sixth but Urshela grounded into a 3-2-3 double play.
Thornton (4-8) allowed one run and three hits in six innings. He walked one and struck out six. Right-hander Sam Gaviglio followed with three scoreless innings.
Yankees: Left-hander CC Sabathia (right knee) felt good after throwing a bullpen before the game. Boone said Sabathia will throw another bullpen Tuesday and could rejoin the Yankees during next week's home series against Cleveland. ... New York put LHP Stephen Tarpley (left elbow impingement) on the 10-day injured list. He is the 27th Yankees player to go on the injured list this season, seven more than in all of 2018. ... Right-hander Dellin Betances (right shoulder) is expected to throw off the mound Monday. ... SS Didi Gregorius got the day off. ... Gary Sanchez was the DH in his second game after returning from injury. Sanchez stayed in after being hit on the left elbow by a pitch from Thornton in the sixth.
Blue Jays: RHP Ken Giles (elbow) played catch before the game and felt good enough that the Blue Jays decided not to put him on the injured list.
Yankees: New York optioned INF Breyvic Valera to Triple-A Scranton/Wilkes-Barre and selected selected right-hander Brady Lail and left-hander Joe Mantiply from Triple-A. OF Giancarlo Stanton (right knee) was transferred to the 60-day injured list to open a spot on the 40-man roster.
Blue Jays: Toronto selected RHP Neil Ramirez from Triple-A Buffalo and optioned RHP Jason Adam to Triple-A. To make room on the 40-man roster, LHP Ryan Borucki (elbow) was transferred to the 60-day injured list. Along with RHP Brock Stewart, promoted Saturday when OF Lourdes Gurriel Jr. (left quadriceps) went on the injured list, the Blue Jays have 10 relievers on their 25-man roster.
Yankees: New York returns home Monday for a doubleheader against Baltimore, as the teams make up for a May 14 rainout. LHP James Paxton (7-6, 4.40) will start the opener, and the Yankees will use an opener in the nightcap. The Orioles will use RHP Gabriel Ynoa (1-6, 5.57) in one game, and have not named a starter for the other.
Blue Jays: Ramirez (0-1, 5.40 with Cleveland) will start against visiting Texas Monday. RHP Ariel Jurado (6-7, 4.74) starts for the Rangers.
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Urshela reacts quickly for diving grab
Randal Grichuk rips a line drive down the third-base line where Gio Urshela immediately dives and makes the catch to end the fourth inning.