Puig delivered a bases-loaded single off the top of the right field wall with two outs in the 10th inning, and Cleveland kept up its playoff push by beating Detroit 2-1 Wednesday night for its 16th straight victory over the Tigers.
The Indians are four games behind first-place Minnesota in the AL Central. Cleveland is a half-game back of Tampa Bay for the second wild card and trails Oakland by 2 1/2 for the top spot.
"I'm feeling good because this is my first walkoff with this team, finally," Puig said, exhaling. "The inning before, I told Lindor and a couple of players, `Hey, I'm going to finish this one with a home run.' I didn't get that, but I got the single to win the game.
"All I'm focused on is my team trying to win the most games we can and waiting for Tampa to lose a couple."
The enigmatic slugger drove the first pitch he saw from Jose Cisnero (0-4) over the head of Travis Demeritte. It was the fourth hit of the game and the fifth career walkoff plate appearance by Puig, acquired from Cincinnati in a three-team trade.
Roberto Perez reached on an error by shortstop Willi Castro to open the 10th and was replaced by Bradley Zimmer, who advanced on Ryan Flaherty's sacrifice bunt. A fielder's choice by Oscar Mercado was bookended by intentional walks to Francisco Lindor and Carlos Santana, setting the stage for Puig.
"You have to take your choice because having to pitch to Puig is not your greatest feeling in the world," said Tigers manager Ron Gardenhire, whose team has the worst record in baseball at 45-106. "With Lindor and the whole package, they have a great lineup and it's stacked at the top."
Puig said he was motivated by the strategy, explaining, "He walked Santana and he's going to pitch to me like I can't finish this game. I got the pitch and put the ball in play and we won."
Adam Cimber (6-3) earned the win with a perfect inning for Cleveland, which did not allow a hit after the fourth.
The Indians' 16-game winning streak over the Tigers is one shy of the franchise record set against Baltimore in 1954. Cleveland is 17-1 versus the Tigers this year, outscoring them 109-38. Detroit matched its longest losing streak against an opponent; first dropping 16 in a row to Minnesota from 2002-03.
"I love this time of year," Puig said. "I've been in the playoffs six times and God gave me an opportunity to come over from Cincinnati to try and make it a seventh time. Oakland is a little far ahead of us right now, but we're right there with Tampa."
The biggest play prior to extra innings occurred in the fourth, when Cleveland left fielder Greg Allen threw out Christin Stewart at the plate on a single by Brandon Dixon. Allen's throw to Perez was clocked at 100.8 mph -- the fastest outfield assist in the majors this season, according to the Indians.
"You know what? Sometimes you surprise yourself whether it's how hard you hit a ball or make a throw like that," Allen said. "I just tried to get the ball out as quickly as possible."
Indians right-hander Aaron Civale worked a season-high 7 2/3 innings, allowing one run. The rookie is the fifth pitcher to begin his career with nine games of five-plus innings and two or fewer earned runs -- the first since King Cole of the Cubs from 1909-10.
Tigers starter Spencer Turnbull struck out eight over five innings, but remained winless in 16 starts since beating Atlanta on May 31. The right-hander leads the majors with 15 losses.
Indians LHP Brad Hand, who is sidelined with a tired arm, threw two dozen pitches in a bullpen session. The All-Star closer last appeared in a game on Sept. 8 at Minnesota. "It was just nice to see him look like himself," manager Terry Francona said. . Cleveland DH Franmil Reyes rejoined the team after spending one day away for personal reasons.
Tigers: 1B Jeimer Candelario (right triceps bruise) was not in the lineup for the second straight day, but entered as a defensive replacement in the ninth inning. He was hit on the arm by a pitch from Baltimore RHP Ryan Eades on Monday.
Indians: 3B Jose Ramirez (right hand surgery) is hitting in the batting cage and fielding ground balls, but Francona is uncertain if he will return this season. The two-time All-Star broke his hamate bone on Aug. 24 against Kansas City.
Tigers: LHP Daniel Norris (3-12, 4.62 ERA) will start the three-game series finale before being relieved by RHP Drew VerHagen. They combined for seven shutout innings, striking out five, in their most recent time-share outing on Sept. 14 at Baltimore.
Indians: RHP Mike Clevinger (11-3, 2.68 ERA) had his 10-game winning streak snapped on Sept. 14 against Minnesota, allowing two runs over a season-high tying eight innings. He is 10-1 with a 2.02 ERA, 118 strikeouts and 23 walks over his last 14 starts.
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