Josh Beckett yielded three hits over eight innings, and Jacoby Ellsbury had an early two-run single for the Red Sox, who won their second straight road game after a franchise-worst 0-7 start away from Fenway Park.
After J.D. Drew and Dustin Pedroia led off the 11th with singles off Rich Thompson (0-1), Gonzalez's drive into right field improved the slow start to his first season with Boston. Pedroia then scored on Jed Lowrie's sacrifice fly to shallow center.
Bobby Jenks (1-1) pitched the 10th, and Jonathan Papelbon earned his fourth save.
Torii Hunter hit a tying two-run homer in the seventh for Los Angeles, which began a seven-game homestand with just its third loss in 12 games.
Beckett opened with five hitless innings against the Angels, who have lost 10 of 11 to the Red Sox since knocking Boston out in the 2009 AL division series.
Boston stranded 13 runners in the first nine innings until Gonzalez came through late.
Boston cleanup hitter Kevin Youkilis left after fouling a ball off his left shin in the first inning. The Red Sox didn't immediately update the condition of Youkilis, who was coming off just his second multihit game of the season.
Rookie Tyler Chatwood allowed six hits and five walks over six innings in his third major league start for the Angels, but left trailing 2-0 after Ellsbury broke open a scoreless game in the sixth.
Beckett threw 125 pitches in his third straight outstanding start for the Red Sox, holding the Angels without a hit until Erick Aybar hit a high-bouncing infield single leading off the sixth, giving Beckett no chance to throw him out.
The former World Series MVP still thoroughly dominated Los Angeles until Hunter broke out of a 3-for-38 slump in dramatic fashion, pounding his fourth homer of the season into the grove of ficus trees in deepest center field.
The Angels returned from a 5-1 road trip in first place in the AL West during their best start since 1993, doing it largely on the strength of dynamite pitching and impressive defense. Los Angeles' hitters had no luck against Beckett, who retired nine straight before Maicer Izturis' leadoff walk in the fourth.
Boston reached base in each of the first five innings against Chatwood, but failed to score each time, stranding seven runners. The Red Sox finally broke through with Ellsbury's short single to right field with two outs in the sixth, scoring David Ortiz and Lowrie.
After Hunter's tying shot, the Red Sox loaded the bases in the eighth on two walks and a hit batter by erratic Angels reliever Fernando Rodney, who settled down and got Pedroia on an inning-ending popup. Aybar then put a drive down the right-field line to lead off the Angels' eighth, but was thrown out trying to stretch it to a triple.
NOTES: Beckett has pitched at least six innings in each of his five career starts at Angel Stadium. ... Longtime Angels closer Troy Percival threw out the first pitch. ... Count Boston manager Terry Francona among those firmly in favor of playoff expansion. Francona supports the much-discussed addition of a second wild-card team to the postseason — or maybe more. "I wish we were hockey," he said. "The more teams, the better. I can't see how it wouldn't be fair." ... Francona is cautiously optimistic top prospect Ryan Kalish wasn't seriously hurt after being taken to a hospital Thursday. Kalish was hurt making a diving catch for Triple-A Pawtucket. Kalish hit .252 during two months with the Red Sox last season.