"It was a nice win for us," Leyland said, "and we kind of got it the unexpected way."
Sixteen of the Tigers' 18 hits were singles, and their only extra bases came on a pair of doubles.
When Polanco's fifth hit of the night scored Edgar Renteria with the deciding run, it marked just the third time this season that they pulled out a game without hitting a home run.
It wasn't the offense many expected out of this team, but in a way, the Tigers showed more offense than they might be expected to muster without the long ball.
"We're a good hitting club," Polanco said. "If we go out and really focus, we can make something happen every day. There are going to be tough days when things don't go your way, but I'm glad it wasn't that way today."
It certainly wasn't in the ninth inning, when a four-run lead was gone and the Tigers needed a run simply to send the game into extra innings.
Mike Lowell's game-tying three-run homer in the seventh inning set up Dustin Pedroia's go-ahead pinch-hit single in the eighth, putting Boston ahead by a run. After Hideki Okajima struck out Gary Sheffield on a hit-and-run for a rally-killing double play to end the eighth, Detroit had to face Red Sox closer Jonathan Papelbon in the ninth.
Not only had Papelbon not blown a regular-season save opportunity since last Sept. 14 against the Yankees, but he had given up just one run in his 12 converted chances since.
Matt Joyce, playing just his second Major League game, started the rally with his legs instead of his bat. His final lunge towards first base was enough to get his foot onto the bag just before shortstop Julio Lugo's throw arrived, giving him a leadoff single. Four pitches and another ground ball later, Lugo seemingly was thinking about a double play and bobbled Renteria's grounder for an error.
With the tying run in scoring position and the winning run on base, the Tigers didn't press. Instead, they played situational baseball. Ivan Rodriguez, whose two-run double in the fifth was Detroit's longest hit of the night, laid down a sacrifice in front of home plate that left Jason Varitek's only play to first.
"He threw one of the hardest fastballs that inning," Rodriguez said, "but I was concentrating to put the ball in play, tried to get a good bunt. For me, it was a little short, but I'm glad that we had two fast runners and they were able to move up one base."
That brought up Curtis Granderson with a chance to win the game with a single, but he had never faced Papelbon in his career. With a hitters count at 2-0, Papelbon got Granderson to pull a ground ball to the right side, but it was deep enough to send pinch-runner Ryan Raburn home and move Renteria to third.
Up came Polanco, who had three singles and a double on the night entering the at-bat. He nearly walked on four pitches, but Papelbon's 3-0 fastball caught just enough for strike one. After swinging and missing at an offspeed pitch to run the count full, Polanco was looking for contact.
When Papelbon (2-1) tried to jam him inside, Polanco got enough contact to end it.
"It was a really good pitch," Polanco said of the fastball. "But sometimes things are going to go your way."
In the Tigers' case, things have rarely gone their way this year, from injuries to key hits. Their .244 average with runners in scoring position was fourth-lowest in the American League entering the night, but they were 6-for-16 Wednesday. Just one of those key hits went for extra bases.
"I'm not going to sit here and say that we just blistered the ball all over the ballpark," Leyland said. "But we did enough to get a win that was important for us."
Said Polanco: "It says a lot about our team. The game is not over until it's over."