Trevor Crowe's suicide squeeze bunt on an eye-high 99 mph fastball scored the go-ahead run in the second game as Cleveland swept a doubleheader from the Tigers, 4-0 and 4-3, on Wednesday night
"It was special for us and for the fans the way we finished," Acta said after Cleveland's sixth straight win.
Right-handers Mitch Talbot and Josh Tomlin both finished their rookie seasons with wins. Tomlin (6-4) went five innings to beat Verlander (18-9) after Talbot (10-13) pitched seven innings for only his third win in his last 13 starts, defeating Max Scherzer (12-11) in the opener.
Crowe's exceptional bunt gave Cleveland a 4-3 lead in the fifth.
"When Verlander has a runner in scoring position, he tends to work his fastball up," Crowe said. "I was looking for it, but not one way up there. You can't practice against something like that."
"You gotta give him a lot of credit," Verlander said. "The pitch was neck-high. He did a fantastic job. He's got to get it down at all costs."
Verlander threw 121 pitches in trying to match his career high in wins set a year ago. He got out of a bases-loaded jam in the seventh by fanning both Crowe and Shin-Soo Choo on fastballs clocked at 101 mph. He struck out 10 overall.
"There were signs of brillance and there were a couple of mistakes made," Tigers manager Jim Leyland said. "It was a kind of a Jekyll and Hyde game for him."
Detroit could not rally against five relievers. Chris Perez got the final four outs for his 23rd save in 27 chances and 10th in a row.
It is the second straight year the Indians finished the home schedule with a makeup doubleheader. They split two games with the Chicago White Sox in 2009 in the final home games managed by Eric Wedge, who was fired with his staff after a 65-97 finish.
Cleveland's 2010 home attendance of 1,391,644 was its lowest since 1,224,274 at old Cleveland Stadium in 1992.
After this sweep, every Indians player and coach tossed a dozen baseballs into the crowd. Each ball had been personally autographed.
"We wanted to leave a lasting impression," Acta said. "What have you done for me lately. We did that with a terrific win and an exciting play."
Cleveland scored on a wild pitch by Verlander in the second and Jayson Nix added an RBI single in the fourth.
The Tigers were without MVP candidate Miguel Cabrera. The slugging first baseman is out for the season with a sprained right ankle, sustained Monday night. He leads the majors with 126 RBIs, is tied for second in the AL with 38 homers and is third in league batting at .328.
Detroit went 1-8 at Progressive Field and 8-1 against the Indians at home. ... Indians right-hander Hector Ambriz will have elbow surgery Friday. ... Cleveland outfielder Shelley Duncan got his first career steal in the eighth inning of the nightcap.