Teixeira has been fighting mechanical flaws for most of the season and came into Tuesday's action hitting just .211, but he was on base in each of his first four plate appearances against Orioles pitching and punctuated the night with a long two-run homer off Matt Albers in the seventh inning.
"It's huge, man," said Swisher, who cracked a two-run shot off O's starter Kevin Millwood among his three hits. "I saw [Teixeira] today and he got a couple of bleeders, and that's kind of what gets you on a roll. He got that and obviously the big home run late in the game. It's coming."
That would be welcome for the Yankees, who have searched Teixeira's body movements and facial expressions for signs of frustration, especially after his rough showing in the Toronto weekend series, which included an 0-for-6, five-strikeout game on Saturday.
"It's kind of like a bounce-back game after you lose a tough game," Yankees manager Joe Girardi said. "When you're in a little streak, you want to bounce back as soon as you can. I think it is important. Tex is a professional and he's not going to let it affect him either way, but as a player, you still want to have those bounce-backs."
Granderson cracked his fourth homer as a Yankee in the third inning, delivering his second career grand slam -- and first since April 4, 2007, with Detroit -- over the right-field wall after Millwood loaded the bases on two hits and a walk.
"I got a pitch out over the plate that I was able to get some good wood on, and it ended up getting out of the ballpark," Granderson said. "I think the offense in general can turn together in a hurry, and we did that again tonight. It's very contagious. Hitting is one of those things."
Making his third start of the season against the Orioles and consecutive starts against the same opponent for the first time in his career, Phil Hughes took advantage of the run support, hurling six innings of three-run ball to pick up his team-leading eighth victory.
That tied him for the American League lead with Clay Buchholz of the Red Sox and David Price of the Rays, but Hughes wasn't satisfied with his showing, admitting he felt he'd picked up a "cheap one."
"My stuff just wasn't great," Hughes said. "Command-wise, I was a little bit off. You have these days and you battle and hope that we do score enough runs. You've just got to tip your cap to them. They took a different approach than they did last game that I faced them. They were more aggressive and didn't let counts get too deep."
Hughes worked out of trouble before the Orioles got him for two runs in the fourth inning, as Matt Wieters and Lou Montanez connected for back-to-back run-scoring singles.
Ty Wigginton knocked in another run with a single off Hughes in the fifth, but that was all Baltimore could get against Hughes, who scattered nine hits, walking none and striking out four.
"I really felt like I wasn't on today at all," Hughes said. "I feel like if I was to evaluate myself without even knowing how many runs I gave up, by the pitches I made, I feel like I shouldn't have won this game."
Tell that to the Orioles. It was still enough to outpitch Millwood, who allowed six runs on 10 hits in 5 2/3 innings and remains winless through 13 frustrating starts this season.
"That lineup did a good job of fouling off pitches, waiting him out, getting the pitch count up early in the game," Wieters said. "You get the pitch count up and you're going to get some pitches to hit."
Brett Gardner dunked a bases-loaded single into shallow left facing Mark Hendrickson in the seventh inning to give New York a four-run advantage. Swisher greeted Albers by clearing the bases with a double to right-center before Teixeira teed off on his blast into the outfield seats.
The only part the Yankees probably could have gone without was seeing Mariano Rivera begin warming up in the ninth inning of what had, at one point, been a 12-3 game. Chad Gaudin struggled in two innings of mop-up relief, hit for four runs on five hits to raise his ERA to 8.53.
"We know that they're going to keep playing and keep playing hard," Girardi said of the Orioles. "We're fortunate that Curtis had a huge hit and gave us a nice little lead. They chipped away and Swish had a big hit. They always play us tough and this is a tough place to play."