The victory put the Tigers up, 1-0, over the Red Sox in the American League Championship Series.
"It would have been nice, but I'll take the win," Benoit said after earning the save by leaving the potential tying run stranded at second base in the ninth inning.
"We wanted to win the ballgame," said Veras, who struck out the two hitters he faced in the eighth inning. "It was nice to get the no-hitter in the ninth, but the most important thing was to get the win and get the lead in the series."
Starter Anibal Sanchez was both erratic and terrific, but he had to come out with a one-run lead after throwing 116 pitches over six no-hit innings, leaving it up to the four relievers to finish the job.
"The entire bullpen did an absolutely fantastic job," manager Jim Leyland said.
The only thing that could have made it better was finishing off the no-hitter. Six times during the regular season, Tigers relievers combined for at least three hitless innings -- that's what it would have taken on Saturday night.
Alburquerque had no idea that a combined no-hitter was a possibility until somebody told him in the ninth.
"Some guy started talking about a no-hitter and I said, 'Oh really?'" he said. "It was probably better not knowing."
After taking over in the seventh, Alburquerque retired the side in order, including two strikeouts. Veras struck out Shane Victorino and Dustin Pedroia to start the eighth, and Smyly got David Ortiz on a fly to center to end the inning.
"Huge out," Leyland said.
That left the ninth for Benoit, but Red Sox outfielder Daniel Nava ruined the no-hit bid. Batting with one out, Nava fouled off three straight 1-2 pitches before lifting a fastball just over the infield for a single to center.
"It was a fastball up and in," catcher Alex Avila said. "Bennie put it in the right spot, but he jammed him just enough for [Nava] to get in there. He made the right pitch, but the guy was able to get through it. If he had hit it on the barrel, he probably would have hit it right at somebody."
After pinch-runner Quintin Berry replaced Nava, Benoit fell behind, 2-0, to Stephen Drew. That prompted a visit from pitching coach Jeff Jones, who wanted to make sure Benoit wasn't too concerned about Berry stealing second base.
"He said, 'Relax and forget about him,'" Benoit said. "Basically, what every pitching coach says in that situation."
Benoit retired Drew on a fly to center. Berry did steal second with Xander Bogaerts at the plate, putting the potential tying run in scoring position, but Benoit got Bogaerts to pop out to end the game.
"When [Berry] was on second, I knew I still had to get the guy out at the plate," Benoit said. "He's not going to steal third. I preferred to focus on making them swing at my pitches."
Benoit, who is in his first season as a closer, was almost involved in a combined no-hitter back in 2002, when as a member of the Rangers he set a Major League record while earning his first career save. Then a rookie, Benoit was being used mainly as a starter, but on Sept 3, in a game against Baltimore, Texas starter Aaron Myette was ejected after just two pitches for throwing at leadoff hitter Melvin Mora.
Todd Van Poppel took over and pitched two hitless innings. In the bottom of the third, with the Rangers leading, 4-0, Benoit came in and did not allow a hit over the next six innings. But the no-hit bid ended when Jerry Hairston led off the ninth with a triple. That was the Orioles' only hit in the Rangers' 7-1 win, and Benoit set a record for the most innings pitched for a save in Major League history.
"This was a totally different situation," he said. "That one doesn't count compared to this one."