Standing at his locker, McAllister cracked a smile when told of Acta's comments.
"That's nice to hear," he said quietly.
Powered by a strong night at the plate from Brent Lillibridge, the Indians' offense gave McAllister sufficient support. The diminutive third baseman churned out three hits, drove in a pair of runs and launched a homer in his best showing in the batter's box in nearly a year.
Indians closer Chris Perez picked up his 31st save of the year with a clean ninth.
The win was the third in the past four games for Cleveland, which continues to try to pick up the pieces after the club's recent 11-game losing streak. One of the main issues during that stretch was starting pitching, though that was hardly a problem with McAllister on the hill against Boston.
"The kid was throwing the ball where he wanted to throw it," Red Sox manager Bobby Valentine said.
McAllister (5-4, 3.46 ERA) turned in eight innings for the Indians (53-61), limiting the Red Sox to two runs on three hits and finishing with four strikeouts and no walks. It marked McAllister's 13th consecutive start with four earned runs or fewer allowed, which is tied for the fourth-longest streak by an American League starter this season.
Only C.J. Wilson (19), CC Sabathia (16), Matt Harrison (14) and Jason Hammel (14) entered Saturday's action having enjoyed longer runs in 2012 among AL starters.
"He's been as consistent as anybody here," Acta said. "It means a lot. You know that you're going to get at least six innings depending on his pitch count. He doesn't walk a lot of guys. He gets himself in position to pitch a good game by attacking the zone with a good fastball and mixing his pitches.
"It's nice to see that. It's great that it's one of those young up-and-coming guys for us."
After the 24-year-old McAllister turned in three perfect frames, the Red Sox (56-59) threatened in the fourth. Jacoby Ellsbury led off with a double and then advanced to third on a botched bunt play. Carl Crawford pushed the ball to the left side, where McAllister and Lillibridge were both racing in.
Indians catcher Lou Marson instinctively shouted for McAllister to throw to third base. The pitcher gloved the ball and looked to third, but no one was covering the bag. Precious seconds were wasted and the pitcher had no play at first base, allowing Crawford to reach safely.
"I heard three and I just reacted," McAllister said. "Given the situation, I definitely should've thrown to first regardless of what I heard. But that's what I heard and I just reacted to that."
Dustin Pedroia followed by chopping a pitch to Lillibridge, who ran Ellsbury back to third base on the play. That kept a run from scoring, but it loaded the bases in the process. Rather than collapsing under the pressure, though, McAllister limited the damage to a two-run double from Adrian Gonzalez.
After that two-base hit, McAllister retired 13 of the final 14 hitters he faced.
"He was dominant the whole night," Acta said. "He ran into a little bit of trouble in that inning where we gave him two extra outs, and he didn't even get rattled."
McAllister felt some relief, considering he allowed nine runs (two earned) in just 1 2/3 innings his last time out.
Lillibridge did his part, falling a triple shy of a cycle.
In the third inning, the third baseman belted a 3-1 pitch from Boston lefty Franklin Morales into the left-field bleachers for a leadoff homer, ending a drought of 124 plate appearances without a home run. It marked Lillibridge's first blast since Aug. 31 of last season, when he was with the White Sox.
Lillibridge finished with his first three-hit showing since Aug. 21 last year and his first two-RBI showing since the Aug. 31 game from a season ago.
"The biggest thing was just getting those runs early," said Lillibridge, who was acquired in a trade with the Red Sox on July 24. "Scoring runs and being a part of the game is always fun."
Lillibridge delivered again in the fifth inning with an RBI single, tying the game at 2.
Michael Brantley used a sacrifice fly to push the Indians ahead in the sixth, and Lillibridge helped provide a key insurance run after opening the seventh with a double. With one out, Marson used a perfectly placed squeeze bunt to score Lillibridge from third base, pushing the Red Sox behind, 4-2.
"That's one of the fun plays in baseball," Lillibridge said. "It was a great job [by Marson] and it was a huge run for us."
It was more than enough for McAllister.
"He gave us a huge lift," Acta said. "He was just fantastic."