''It was the highlight of the day,'' Padres catcher Yasmani Grandal said. ''He looked back at the umpire and said we were cheating, and the umpire started laughing.''
Despaigne came within four outs of the first no-hitter in San Diego's 46-year major league history on Sunday, and the Padres beat the New York Mets 2-1 on Seth Smith's run-scoring infield single in the ninth.
Making his fifth major league start, Despaigne didn't allow a hit until Daniel Murphy doubled to left-center with two outs in the eighth.
''I thought I threw him a pretty good pitch,'' Despaigne said through Grandal, who served as his translator. ''I did great with all my pitches, attacking after getting the first strike.''
San Diego, the only active major league franchise without a no-hitter, was playing its 7,264th regular-season game and has played 34 more in the postseason.
The Mets were the only other active big league team without a no-hitter before Johan Santana pitched one against St. Louis in June 2012 during New York's 8,020th regular-season game.
Despaigne, a 27-year-old Cuban right-hander signed as a minor league free agent on May 2, allowed one run and two hits in 7 2-3 innings with five strikeouts and three walks. He threw 123 pitches and lowered his ERA to 1.31.
''I thought he was throwing well enough to think, 'Hey, it could happen,'' Padres manager Bud Black said. ''He had all four pitches working from different angles. His stuff was good enough to keep them off-balance.''
His was the longest no-hit bid by a single Padres pitcher since Sept. 7, 2008, when Chris Young allowed a two-out home run in the eighth to Milwaukee's Gabe Kapler.
''I think we saw in the fourth time through the lineup we started having better at-bats,'' Murphy said. ''I got the base hit, David got the base hit. So the next time we'll have a better idea.''
Despaigne threw a fastball above 90 mph, a slider in the 80s, a changeup in the 70s and a curveball in the 60s.
''When you vary your speeds from 65-to-93, that's tough to get a good pitch to hit,'' Mets manager Terry Collins said.
Murphy scored on David Wright's single to tie the score 1-1.
Vic Black (2-3) walked Carlos Quentin on four pitches leading off the ninth, and Alexi Amarista bunted, with pinch-runner Cameron Maybin advancing to second and Amarista reaching when the ball went through Black's legs for an error.
Chase Headley grounded into a 4-3-6 double play as Maybin reached third. Josh Edgin relieved, and the pitcher tumbled to the ground when he came off the mound to field Smith's bouncer between the mound and first.
Edgin dropped the ball, picked it up and then shoveled it to first too late to catch Smith as Maybin came across the plate.
''When it went off the bat I didn't know if it had a chance to bounce over him or not,'' Smith said. ''Once it leaves your bat, all you can do is run and that is what I did.''
Joaquin Benoit (4-2), San Diego's fourth pitcher, threw a perfect ninth for the win.
New York scored one run in the last 18 innings of the series and has lost two in a row following a 9-2 spurt.
Grandal homered in the fourth off Zack Wheeler, who allowed one run and eight hits in six innings with seven strikeouts and a walk.
NOTES: Collins said RHP Daisuke Matsuzaka could step in if LHP Jon Niese's start is cut short in Seattle on Monday. With Neise's return from the DL, Matsuzaka will work out of the bullpen but is available for a spot start. ... Collins said OF Bobby Abreu started on Sunday to prepare him for the DH role in Seattle. Abreu is 0 for 18 as a pinch hitter. ... Padres SS Everth Cabrera (strained left hamstring) is to play Monday with Triple A El Paso. ... RHP Andrew Cashner (right shoulder strain) threw again on the side but will rest on Monday. ... Niese (5-4, 2.96) faces Mariners LHP Roenis Elias (7-8, 4.54) on Monday. Padres LHP Eric Stults (3-11, 4.98) goes against Cubs RHP Kyle Hendricks (0-0, 6.00) on Tuesday in Chicago.