"I saw a guy who left every ounce of what he had out there," said Red Sox manager Terry Francona. "A lot of hits, and a refusal to give in. I thought we saw the guy that we've come to depend on."
With the defeat, Beckett fell to 16-6.
And with the win, the Yankees closed the gap to six games in the American League East. It will be up to Curt Schilling to prevent a sweep when he takes the ball for the Sox in a Thursday matinee against Chien-Ming Wang.
"We just have to keep on trying our best," said Red Sox slugger David Ortiz. "Even when those guys were struggling, I knew it wasn't going to be like that all year long. Dude, they have so much talent. They have talent all over the place."
Clemens, who looked like a young 45 on this night, had a no-hitter through 5 1/3 innings. Ortiz ended that bid by putting one over the wall in right in the sixth.
Will Ortiz still be clearing walls at the age of 45 just like the Rocket is still slinging heaters?
"At that age, I'll be cutting grass in my backyard," laughed Ortiz. "You have to give a lot of credit to that guy. To be pitching at that point of his career, that's a lot of preparation. It's hard, bro. In this game, when you turn 30, your body starts changing. You have to start working. When you turn 40? Ask [Tim Wakefield]."
For Beckett, the 13th and final hit allowed was by far the unluckiest. That was the one Alex Rodriguez lined over the wall in left to make it 4-1 in the sixth.
The breaking ball caught too much plate, and A-Rod -- who now has 44 home runs -- knew what to do with it.
"It all comes down to really one pitch," said Beckett. "The home run to Alex. Stupid pitch, stupid spot to a smart hitter."
Kevin Youkilis belted a two-run homer off Kyle Farnsworth with nobody out in the eighth to pull the Red Sox to within a run. Youkilis shouted with emotion as he rounded first, thinking the Red Sox might have gotten the big hit they needed.
"You think we might get some spark there and come back and win it," said Youkilis. "We just didn't. You have to tip your cap to Mariano [Rivera]. He came in and threw well."
Rivera recorded the final four outs for save No. 22, retiring each batter he faced.
"I don't ever want to see him come in a game," Francona said. "First of all, it means we're probably losing. Never been real thrilled when he's in the game."
A three-run rally by the Yankees, achieved with two outs in the second inning, was perhaps the biggest difference in the game. With runners on first and second and two outs, Melky Cabrera ripped an RBI single up the middle. Johnny Damon, the hero from Tuesday night, slapped a two-run single to left to give Clemens a 3-0 lead.
"One big inning," said Red Sox catcher Jason Varitek. "Johnny did a nice piece of hitting. That was a huge difference."
Beckett hung tough. With the bases loaded and two outs in the sixth, he got out of trouble by getting Damon on a grounder to first. Beckett helped complete the play, outracing Damon to the bag.
"That's what good pitchers do," said Youkilis. "You watch Greg Maddux, they don't throw no-hitters; they give up hits, and get out of jams. That's what the best pitchers do. They know how to get out of jams when they need to."
But Beckett couldn't jam A-Rod when he needed to, and that was his final pitch of the night.
"I didn't want to come out," said Beckett. "I battled that far. That's not my job. [Francona] makes those decisions. My job is to execute pitches as best I can until the game is over or somebody takes the ball out of my hand."
The Red Sox will try to get some momentum back on Thursday, when they will again be without Manny Ramirez, who has a strained left oblique.
"Every game is important," said Sox second baseman Dustin Pedroia. "Not just [Thursday]. We have 29 games left? Hopefully we go out there and win them all. It's not like the season is over if we don't win tomorrow."
As for Clemens, you wonder if his career will ever be over.
"He knows what to do with the baseball," said Varitek. "He always has. He was a little different than what we've seen on tape. He had a little more power today. He was able to throw strike one a lot."