Cabrera hit a game-ending solo homer in the ninth inning and the Tigers beat the Chicago White Sox 2-1 on Thursday to complete a three-game sweep.
"Leyland told me before the game to try to hit a home run and be a hero," Cabrera said. "It feels great. We won and we swept the series."
The sweep came after an embarrassing 8-2 loss to Cleveland that ended with Dontrelle Willis demoted to Class A.
"These are still baby steps, but we've taken three straight baby steps," Leyland said. "We have to start playing well enough to get people talking about us again."
The big-budget Tigers are still eight games back of the AL Central-leading White Sox.
"The standings are always important until you are in first place," Magglio Ordonez said. "We've still got to catch them."
Ordonez led off the bottom of the ninth with a long drive to left, bringing the sold-out crowd to its feet, but Carlos Quentin made the catch at the wall. Cabrera then hit a 2-1 pitch from Octavio Dotel (3-3) into the stands in right-center field.
Cabrera's ninth homer of the season came after a pitching duel between Detroit's Kenny Rogers and White Sox left-hander Mark Buehrle. Both starters allowed one run in eight innings, and the game lasted just 2 hours, 4 minutes.
"I knew I was going to have to work quick, because Mark pitches so fast," the 43-year-old Rogers said. "I felt good today, and I'm healthier than most of the guys in this clubhouse right now."
Rogers has gotten a no-decision in each of his past four starts, despite going at least seven innings in each outing and only allowed four earned runs.
"He's been fantastic for us lately," Leyland said. "He's given us everything we could possibly want."
Buehrle gave up seven hits, walked one and struck out six. He has allowed just one run in four of his past six starts.
"I threw the ball well today, but it was just one of those things," he said. "Now I just have to go out and prepare for my next start and see what happens."
Detroit tied it at 1 in the sixth. Carlos Guillen singled in Edgar Renteria with one out, putting runners on first and third. Buehrle then got Ordonez to pop out and retired Cabrera on a fielder's choice to end the inning.
"He's so good because he changes so many things on you," Ordonez said of his longtime Chicago teammate. "He'll come in, come in and then go out, and he's going up and down, and he's quick. He's tough."
Chicago took the lead in the second inning. Paul Konerko hit a leadoff double into right-center field and advanced to third when right fielder Ryan Raburn misplayed the carom. Jermaine Dye followed with a sacrifice fly to center.
Quentin started the ninth with a single off Todd Jones (2-0), but Konerko grounded into a double play.
"We pitched well and they pitched well, but they got the big hits and we didn't," Chicago manager Ozzie Guillen said. "That was the story of the game. Hopefully we can go home and get the bats going again."
Rogers gave up four hits, walked one and struck out one.
- Detroit right-hander Eddie Bonine will make his major league debut when he starts Saturday against the Dodgers, replacing Willis in the rotation. "I've never seen him, but he's 24-5 in the last couple years, and if that isn't enough to get you called up, I don't know what you would have to do," Leyland said.
- The White Sox have now lost six straight road games while winning their past eight at home.
- Tigers catcher Vance Wilson is considering retirement after reinjuring his throwing elbow. Wilson had Tommy John surgery to replace a torn elbow ligament last June, but tore the transplanted ligament while rehabbing the injury, and faces another year on the sidelines.