Wade bounced back from a loss in the series opener on Monday, in which he served up a game-winning ninth-inning home run to Mark Trumbo, by striking out three of the four batters he faced on Wednesday.
Trumbo homered for a fourth straight game, this time off Yankees starter Ivan Nova, who allowed five runs in 6 2/3 innings. But New York was able to hold a lead created by Raul Ibanez's triple and Nick Swisher's sixth-inning sacrifice fly.
"It's the difference in the game, what our bullpen did," Yankees manager Joe Girardi said. "A nice job by everybody."
Soriano made the Yankees sweat a bit in the ninth but secured his sixth save in six opportunities since taking over the closer's role vacated first by Mariano Rivera's season-ending right knee injury and then by David Robertson's strained left oblique.
"It's not the most stress-free win, but you're playing a tough team," catcher Russell Martin said. "They were hot and we just did enough to put out the fire."
Alberto Callaspo worked a one-out walk to put the tying run on base and Albert Pujols reached on an infield single that Derek Jeter made a diving stop on to keep runners from going to the corners.
After a fielder's choice, Soriano threw a 3-2 slider that exploded Trumbo's bat, resulting in a weak fly ball to left field.
"I've seen how [Trumbo has] been doing all three games," Soriano said. "To me, I make a good pitch and see what happens."
Trumbo, who finished 3-for-4 with three RBIs, said he was due to miss an opportunity.
"Tough at-bat, tough out," Trumbo said. "They're not all going to fall. If you can go away and feel like you gave it your best effort, you can sleep a lot easier at night."
Nova was upset with his performance in a troubled start, as he was hit for five runs in 6 2/3 innings, including a four-run fourth that wiped away an early lead.
"I'm not pitching good right now," Nova said. "I mean, it's hard when ... you know that you're better than what you're showing right now. It's really hard for me. So I think I've got to enjoy this win today, the team win, that's the most important thing."
The Yankees built an early lead off Angels starter Ervin Santana as Curtis Granderson hit a three-run homer, his team-leading 16th, and Robinson Cano blasted a two-run shot for the Yankees.
"It was a tough inning," said Santana, who has allowed a Major League-leading 15 homers. "I got behind in the count in that inning almost to everybody, and it's not easy to get behind in the count against these guys because they're good. They make adjustments quick enough."
Provided with a 5-1 lead by the third-inning barrage, Nova ran into trouble in the fourth as Trumbo homered and Mike Trout wrapped up an impressive series with a two-run, game-tying double.
The blast to right field made Trumbo the first Angels player to homer in four straight games -- including all three of the series against the Yankees -- since Rex Hudler in 1996.
Nova settled down and pitched into the seventh, scattering eight hits while walking three and striking out two.
"I know at some point this year, I'm going to start pitching better, and I hope it's going to be soon," Nova said. "I still have a lot of confidence in myself and I know I can get out of bad situations."
But he had to watch from the dugout that inning as his decision -- his second consecutive victory -- hung in the balance.
Looking to turn around switch-hitter Kendrys Morales, who has struggled against left-handers this year, Girardi opted for Boone Logan over Nova.
Morales singled, as did Trumbo, and Wade was summoned for arguably the biggest out of the night as Kendrick struck out swinging.
"It's huge. I guess that's the advantage of being a reliever," Wade said. "To be able to go out there and redeem myself felt good."