The Yankees were staring at a quick first inning against starter Aaron Cook (2-4) when Teixeira ran hard to first base on a grounder, beating shortstop Mike Aviles' throw as Granderson scored to tie the game.
Ibanez followed by chasing a Cook offering up and away, smashing it over the right-field wall for his 13th home run. The blast gave the Yankees a quick lead, one they'd hold for the rest of the contest.
"After the home run, you realize it was a three-run play," Teixeira said. "You don't take pride in making an out, but getting an RBI there and extending the inning was big. But Raul gets the credit. I just ran hard and Raul did the rest of the work. That two-run homer was huge."
Ibanez said of Teixeira's effort, "It really fires everybody up. He was hustling from the moment he hit that ball, trying to keep the double play from happening so the run could score. Then as a hitter, you get the opportunity, and try to do what you can with it."
New York's victory was completed in a rapid two hours and 41 minutes, the quickest Yankees-Red Sox game since Sept. 11, 2005 (2:29). It also swelled Boston's deficit in the American League East to a season-high 11 1/2 games.
The Red Sox have lost six of seven games, but the Yankees consider these important wins, not wanting to count Boston out with 62 games still remaining on the schedule.
"We know we're better than this," Boston's Cody Ross said. "We have a ton of talent, but talent doesn't win ballgames. You got to go out there, manufacture and play the game the right way and we're just not doing that."
Cook was hit for six runs and seven in four innings. Teixeira added a sacrifice fly in the third inning and the Yankees added two more in the fourth on Martin's 11th homer, a blast to left field.
Granderson put the game out of reach in the eighth as he connected for his fifth career grand slam and second of the season, delivering off Mark Melancon.
"We were able to string together some home runs and put some runs on the board," Ibanez said.
Hughes (10-8) was taken deep three times, but he limited the damage, walking one and striking out five as he scattered five hits in a 110-pitch effort.
"I tend to overthrow a little bit sometimes, especially early in the game," Hughes said. "I've talked about it before, just trying to settle those nerves and be smart out there from pitch No. 1. I'll continue to work on that."
Manager Joe Girardi admitted to wondering if he'd be able to squeeze a quality start from Hughes in a 28-pitch first inning that featured Dustin Pedroia's homer, even as Hughes struck out Jarrod Saltalamacchia to strand two runners in scoring position.
"You're thinking, 'It's going to be tough to get seven innings out of him, and it might be tough to get six,'" Girardi said. "But he settled down nicely and went right to work."
Carl Crawford launched his first homer of the year -- a second-deck blast to right field -- off Hughes in the third. Saltalamacchia produced the third Red Sox run with his 20th home run of the season, a fourth-inning blast to left.
But Hughes held Boston quiet from there, retiring eight straight before turning the pitching over to David Robertson for the eighth. Cody Eppley pitched the ninth with a seven-run lead.
"It's nice to get some runs early," Hughes said. "Knowing you have a lead to work with, you just try and keep baserunners off base. Sometimes the homers happen, but as long as they're solo homers ... with our offense I feel pretty good about what we can do if I'm just keeping guys off base and staying aggressive."
There have been plenty of reasons why the Yankees enjoy such a commanding advantage over their rivals at this late date in the schedule, against whom they're 6-1 this year. But on this night, the Yankees didn't want to overlook small contributions like running out a routine ground ball.
Teixeira said he still hears platitudes from fans wondering why he ran so hard on a 2009 Alex Rodriguez popup, scoring after Mets second baseman Luis Castillo lost the ball in the evening sky. Friday's charge down the first-base line might not be as well remembered, but it was certainly appreciated.
"I've always hustled, you know," Teixeira said. "My dad, when I was a kid, never got mad at me for striking out or popping out or making an error, but if I didn't hustle, that's when he would get on me. I think it was just a lesson I learned as a young kid. I don't have a lot of speed, but I try to use as much as I have."