But amid an otherwise brilliant performance by the Boston right-hander in a 10-5 victory, that bid ended on a clean single to right by Curtis Granderson with two outs in the bottom of the seventh inning.
With the count 2-1, Granderson thumped a 94-mph fastball through the hole on the right side and easily into right field for a hit.
"It was a sinker down the middle," said Beckett. "He hit it good. It wasn't a very good pitch."
Some deflation, perhaps. But Beckett didn't let it affect his concentration on a night he allowed two hits and three unearned runs over 7 2/3 innings, walking two and striking out nine.
"I was trying to stay pitch to pitch," said Beckett. "It was a tight game at that time. I was just trying to get outs."
The only Tigers batter to come close to getting a hit in the first six innings was catcher Gerald Laird, who attempted to bunt leading off the sixth, but the ball just rolled foul.
Laird eventually struck out looking. Beckett hit him with a pitch when he came to bat again in the eighth.
Third baseman Mike Lowell, who has been teammates with Beckett longer than any other member of the Red Sox, got his hopes up.
"He was spectacular," said Lowell, who has played with Beckett in Florida and Boston since 2001. "I know there's a little bit of luck and everything, but he had such good stuff, I really thought there was a chance he was going to throw a no-hitter. Once he got past the sixth, I was like, 'Nine more outs.' You're kind of counting them down. I thought he was outstanding."
Though Beckett didn't come quite as close as Tim Wakefield on April 15 at Oakland (7 1/3 innings), it was a standout performance. The Red Sox have been no strangers to no-hitters in recent years, as Clay Buchholz fired one in 2007 and Jon Lester notched one last year.
"He looked great," said Red Sox second baseman Dustin Pedroia. "Kind of felt like he was going to throw a no-hitter. He had no-hit stuff. It's good to see him throw the ball like that. He dominated."
Beckett, who has never thrown a no-hitter, doesn't remember any other near-misses.
"I think I took one into the second one time before this," quipped Beckett. "I don't know, but it wasn't very deep I don't think."
More vital for Beckett and the Red Sox (31-22) is that the power righty has turned in six consecutive quality starts to run his record to 6-2 and lower his ERA to 4.09.
"I'm locating my fastball, and good things are happening," Beckett said. "We've been working hard and really just trying to get back to the things that make me successful. It doesn't hurt me that we can score that many runs and play great defense."
Once the no-hitter ended, the Red Sox broke the game open, notching a six-spot in the eighth, fueled by two-run doubles by David Ortiz and Jason Varitek.
For Ortiz, who is hitting .187 with one homer after a 1-for-4 night, it was a little redemption after his fourth-inning drive, which traveled roughly 420 feet, was flagged down at the wall in left-center for an out.
"I don't know how much better you can hit a ball," said Red Sox manager Terry Francona. "That ball was as good a swing as he's taken in a long time. This ballpark will do that, especially on a night like tonight."
Things got chaotic in the bottom of the eighth, when the Red Sox made three errors and allowed the Tigers (28-23) to score five unearned runs. Making matters worse, first baseman Kevin Youkilis, trying to finish a double play, got kicked in the right ankle by Josh Anderson in that inning. Though Youkilis came out of the game, he is expected to play Thursday afternoon.
"He's OK," Francona said. "He got more of a bruise. I think all our fears were that he got spiked and then everybody got up from the replay and said he kind of got kicked with the back foot. He said he'll be OK [for Thursday]."
The new 1-2 punch of Pedroia and J.D. Drew paid off right out of the gate in this one. Pedroia led off the game with a single up the middle and Drew followed by clubbing a two-run homer to right. It was No. 200 of Drew's career, and it gave Beckett a 2-0 lead before he even threw a pitch.
Through six, Beckett had thrown just 74 pitches and faced one batter over the minimum. After he walked Magglio Ordonez with one out, Miguel Cabrera blasted one to the gap in right-center, but Jacoby Ellsbury raced back to catch it. But Granderson hit a 2-1 pitch into right field, snapping Beckett's bid at the no-no.
"I thought [Beckett] was tremendous," Francona said. "We scored early, then we scored again and we spread it out, which is always a good formula. But his stuff, from the first hitter of the game, you could see -- he was commanding his fastball, he threw some real good changeups, he threw some good breaking balls. He was confident in his delivery. There was no muscling. The ball had great movement. That was really fun to watch."
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.