"I liked the way we battled today against this ballclub, and especially against the pitcher we went against," Acta said.
"A lot of credit goes to David Huff, who pitched a tremendous ballgame, despite warming up twice because of the rain situation," he said. "He really made some good pitches when we didn't play good defense behind him and made him throw a ton of extra pitches. He really buckled up and made some great pitches. I can't say enough about him — he gave us a tremendous outing."
Pinch-runner Jarrod Saltalamacchia dived across home plate to score the winning run on Jacoby Ellsbury's single in the ninth inning.
Ellsbury then singled, setting up the play at the plate. Center fielder Eziquiel Cabrera made a wide throw home and Carlos Santana caught the ball, but Saltalamacchia won the race to the plate.
The start of the game was delayed by rain for one hour, 35 minutes.
Huff, making his third start since being recalled from Triple-A Columbus, lowered his ERA to 0.51 with five innings. The only run that scored against him came after an error by second baseman Jason Kipnis.
The run actually scored on a wild pitch by Huff on strike three to Jason Varitek, the first of three straight Ks by Huff to get him out of a bases-loaded, one-out jam with only one run scoring.
"At the end, they came back and beat our bullpen, which has been our strength so we have to give them credit," Acta said. "They pieced three hits together at the end there, one on a broken bat, there's not much you can do. I just like the way we're fighting right now."
Jonathan Papelbon (3-0) got the win after shutting down the Indians on just 10 pitches in the ninth. Boston posted its six walk-off win of the season.
Jason Kipnis and Lonnie Chisenhall hit solo homers for Cleveland's runs. Chisenhall homered into the right-field corner in the fourth.
Youkilis tied it at 2 with a towering solo shot that hit one of the signs above the Green Monster.
Youkilis was ejected after his next at-bat, when he struck out on a checked swing and argued on his way back to the dugout.
Kipnis, who homered in his last at-bat Monday, drove the first pitch he saw from Beckett into the Boston bullpen in the first to put the Indians up 1-0.
Beckett was pulled after six innings, allowing six hits and striking out seven.
NOTES: Indians RHP Carlos Carrasco said he planned to drop his appeal of a six-game suspension after he starts against the Boston Red Sox on Wednesday night. Carrasco was suspended and fined $2,500 for throwing at the head of Kansas City's Billy Butler last week. Newly acquired Ubaldo Jimenez will start Friday night at Texas and the Indians are off Monday, giving them some flexibility with their rotation. ... Red Sox SS Marco Scutaro, who left Monday night's game with dizziness, was sent for tests Tuesday that cleared him to play, but he was held out of the starting lineup by manager Terry Francona. Scutaro entered the game in the ninth inning after Youkilis' ejection. Mike Aviles, who started at short, moved over to third. ... Injured Boston SS Jed Lowrie is playing rehab games at Triple-A Pawtucket, where he went 1 for 3 Tuesday and could return soon.