Teixeira, who left in the offseason to sign a free-agent deal with the Yankees, went 1 for 5 and stranded four runners. He was showered by boos throughout the game.
Aybar, one of the smallest players in the Angels' clubhouse at 5-foot-10, provided the spark for the Angels, who are missing Torii Hunter (adductor strain) and Vladimir Guerrero (strained muscle), who both went on the disabled list earlier in the day, and Juan Rivera because of injuries.
"You don't see Erick hit home runs very often, you don't see him miss one by a couple feet foul and then come back and hit one," Angels manager Mike Scioscia said. "Two good at-bats and we needed them."
Alex Rodriguez homered for the Yankees, who failed to extend their eight-game road winning streak despite taking a 4-0 lead in the second and fell out of a first-place tie in the AL East with the Boston Red Sox.
"We swung a notch above and got back into the game," Scioscia said.
Gary Matthews Jr. had an RBI single in the second for his 1,000th career hit, and Bobby Abreu drove in a run in the fifth to cut the Yankees' lead to 5-2. Morales then hit the first pitch he saw from Yankees starter Joba Chamberlain over the wall in center field for his 15th homer, tying the game at 5.
Chone Figgins' RBI triple in the sixth gave Los Angeles a 6-5 lead.
"How about that?" Matthews said. "I guess I only got 1,011 more to catch my dad. I should be about 46 by the time I get there."
Chamberlain, coming off one of his worst starts of the season where he gave up a career-high eight runs, allowed the run in the second before imploding in the fifth.
He pitched 4 1/3 innings and gave up five runs -- four earned -- and nine hits.
"It's frustrating. I'm letting my teammates down, so it's kind of embarrassing, too," Chamberlain said. "I'm doing everything I can between starts, going out every day and continuing to work my tail off to get better to help this team, and I'm not getting results. The last two starts is the best my stuff has been all year, which makes it even more frustrating."
Mike Napoli reached when shortstop Derek Jeter dropped a popup in the seventh and Jeff Mathis was walked by Brian Bruney. With two outs, Aybar connected to deep right to make it 10-6 with his third homer of the season.
"I've never seen it, and I doubt we'll ever see it again," Yankees manager Joe Girardi said of Jeter's error. "It's a first for me. I mean, he's so great on popups. I was completely shocked. They ended up scoring three runs, and it looks like we're out of the inning if we don't do that. I mean, that makes it a big difference going into the ninth inning."
"We gave them extra outs. The extra outs killed us. When you're playing that team, you can only give them three outs an inning," Jeter said. "They took advantage of a couple of mistakes and scored a lot of runs. They're not going to beat themselves. They put pressure on the defense and they pitch well."
Angels starter Joe Saunders continued to struggle with his command, giving up the four early runs.
"I think it's a step forward for Joe. I liked his stuff," Scioscia said. "Hopefully he'll be able to fine tune it a little bit and have it be a little more effective next start."
Jeter, who was 4 for 5, hit the first pitch for a leadoff single in the first and Johnny Damon was walked after starting the at-bat with an 0-2 count.
Rodriguez hit a double to score both runners and Nick Swisher had an RBI single off Saunders, who gave up nine hits and five runs in five innings.
Damon drove in a run in the second, and Rodriguez hit his 15th homer in the fifth to make it 5-1.
Melancon was recalled from Triple-A Scranton before the game to replace RHP Jonathan Abaladejo. ... The Angels recalled INF Brandon Wood and C Bobby Wilson from Triple-A Salt Lake. ... Rivera left the game with tightness in his left quad and right hamstring.