Hafner went 1 for 3 with two walks in his first game since having right knee surgery May 31.
Lowe (8-6) gave up three runs and 11 hits in six innings for his first win in six starts since June 1. The 39-year-old was 0-3 with a 7.71 ERA in five outings between victories.
"It's great to see the guys get a lot of runs," Lowe said. "Then it's up to me not to walk guys and give it back."
Michael Brantley hit a three-run homer in the first inning off Ervin Santana (4-9) and Casey Kotchman had a three-run shot in a six-run second as Cleveland took a 9-1 lead.
Johnny Damon had a season-high three of Cleveland's 14 hits. The Indians totaled 21 runs in two wins after being shut out 3-0 in the series opener.
"We had a lot of quality at-bats and you could see Hafner's effect right away," Indians manager Manny Acta said. "He just wore out Santana and then Brantley hit that homer."
With two outs and Jason Kipnis on first with a walk, Hafner drew an 11-pitch walk. Brantley followed with his second homer for a 3-0 lead.
"Brantley got a good pitch to hit," Damon said. "Certain players (Hafner) make others around them better."
The Angels loaded the bases with no outs in the second, but scored only once.
Lowe threw a called third strike past Erick Aybar before Maicer Izturis grounded into a run-scoring forceout. With runners on first and third, Jack Hannahan ranged behind the bag at third to get a grounder hit by Bobby Wilson. His long throw got the slow-running catcher by a step at first for the third out.
"That was huge," Acta said. "Guys with that power sinker are always one pitch away from doing that, getting the ground ball. He made 18 first-pitch strikes and knows how to pitch with a lead."
Lowe said getting Aybar relieved some of the pressure.
"The biggest pitch was the 3-2 curve for the strikeout," he said. "But pitching in games like this isn't always easy. You afraid to nibble and walk guys, but don't want to throw it down the middle, either."
Cleveland made it 9-1 in the bottom half. Shin-Soo Choo had an RBI double and Asdrubal Cabrera a run-scoring groundout. First baseman Albert Pujols fielded Cabrera's ball, but dropped it before he could throw home and settled for picking it up and stepping on the bag for the out. Choo took third play and scored on Kipnis' single for a 6-1 lead.
Santana left after Hafner singled Kipnis to second. The right-hander allowed eight runs and six hits over 1 1-3 innings and fell to 1-8 with a 5.03 ERA in 13 starts against Cleveland. The win was a no-hitter at Progessive Field last July 27.
"Obviously, a rough outing," Angels manager Mike Scioscia said as Santana dropped to 2-4 with a 7.45 ERA on the road this year. "We need Ervin to pick it up. He's a guy we're counting on in our rotation."
Reliever Hisanori Takahashi came on and got one out before Kotchman hit a three-run homer to right.
Pujols had a strange series, despite going 3 for 9 with a homer in the three games.
He went 1 for 3 against Lowe, but was out trying to stretch a single to a double in the third, trailing by eight runs. He hustled of the batter's box, but was out by yards at second on a throw by Damon -- not known for a strong throwing arm.
Damon exchanged high-fives with fans after the play.
"I threw and a fan yelled, `Great throw,' and I said, `No, I left it up,' " Damon said. "I was talking and the guy said, `He's out!' I looked at second base and said, `You're absolutely right.' I had no clue."
Later, Pujols hit a high drive that drew oohs and ahhs from the crowd. The ball died in the humid air and plopped into Damon's glove at the warning track as Pujols stood with head cocked, hands on hips, staring in disbelief.
Tuesday night, Pujols made a crucial throwing error that enabled two runs to score in the Angels' 9-5 loss. And on Monday night, he over-ran second base on a wild pitch and was thrown out.
Alberto Callaspo had a sacrifice fly and Izturis an RBI single in the Angels' sixth.
NOTES: The victory margin was Cleveland's largest since beating the Chicago White Sox 11-2 on May 22, 2011. ... Cleveland is hitting .325 over its last nine games. ... Lowe is 5-1 with a 2.86 ERA at home. ... Marson has hit .393 (24 of 61) since May 20, raising his average from .074 to .295. ... Scioscia pulled many regulars in the sixth amid mid-90s temperatures and high humidity. ... RHP Dan Haren will be examined Thursday in Los Angeles. After allowing seven runs in 4 1-3 innings Tuesday, he said his back has been bothering him all season. ... Angels OF Vernon Wells, out since having right thumb surgery May 21, will begin hitting drills next week. ... Cleveland placed OF Shelley Duncan on the paternity list. His wife is expecting twins.