The four relievers took over for Rick Porcello with one out in the sixth and combined for 2 2/3 scoreless innings to preserve a one-run lead.
It became a two-run lead when Andy Dirks, hitting in the No. 2 spot, lofted a ball over the right-field wall in the eighth inning. The Tigers scored three runs and all three came on homers. Dirks wasn't the longest, but Leyland said it was the most important.
"That changed the dimension of the game," Leyland said.
It meant Valverde had some breathing room in the ninth. Technically, it wasn't needed, but the Tigers were happy he had it when the first runner reached and moved into scoring position.
Alex Rios singled and stole second right away. The 34-year-old Valverde bounced back to strike out Alexei Ramirez, but walked Kosuke Fukodome to bring the go-ahead run to the plate. Pinch-hitter A.J. Pierzynski hit a soft popup to third, and Valverde battled back from a 3-0 count to strike out Beckham for the save.
Porcello, who picked up his second straight win to improve to 3-2, was asked if there were any nerves watching Valverde. He smiled, but quickly answered, "No".
"I have a lot of confidence in Papa Grande," said Porcello, who pitched 6 1/3 innings of four-hit, one-run ball while walking two and striking out five. "That's how I was feeling."
The 23-year-old right-hander continued utilizing his tweaked windup. Rather than keep his hands down, he's bringing the glove over his head to help keep the location of his pitches down. He said it's a permanent switch and that repetition is making it more comfortable.
"Surprisingly, we tried it in the bullpen in New York and it felt a little weird," Porcello said. "But then the next day, I went into it again and it felt a lot more natural the second time around. So it really didn't take that long to feel natural."
Porcello induced nine groundouts compared to four flyouts, so it's clear the move has helped. And Porcello isn't the only Tigers pitcher to tweak his delivery.
Max Scherzer adjusted the placement of his hands and saw instant results on Saturday. Leyland said the pitching coach doesn't usually get noticed unless there are problems, but all three gave Jeff Jones a lot of credit.
"Jonesy's a great pitching coach," Porcello said. "He sees a lot and he's extremely helpful when it comes to certain things like that in your delivery to consistently execute pitches. He's been a big factor."
Porcello's only trouble came in the first inning, when Adam Dunn hit a solo shot over the gate above the right-field wall. However, Austin Jackson immediately responded in the bottom of the frame with his fourth home run off White Sox starter Dylan Axelrod.
Prince Fielder, who hadn't homered in Comerica Park since April 7, blasted one 432 feet to right-center in the third inning to break the tie.
"It was one of the farthest and one of the hardest and one of the lowest probably [I've seen]," Leyland said. "I could tell the trajectory of it. It was just going right through everything."
All of the game's runs came on homers, but both clubs squandered opportunities. Detroit left 12 runners on base, including the bases loaded in the seventh, and went 1-for-10 with runners in scoring position.
The White Sox stranded eight runners and went 0-for-8 with runners in scoring position.
"We played neck-and-neck all three games and we just obviously didn't get the big hit to either tie it or put us up," Dunn said. "Overall, we played good. Just obviously not good enough."
With Sunday's two-run victory being the largest margin of the three-game series, it's clear the Tigers played just good enough.