SAN DIEGO (AP) -- After 7,582 games since 1969, the San Diego Padres still don't have a no-hitter.
Edwin Jackson, of all pitchers, was the latest to try to pitch an elusive gem - in his Padres debut, no less.
Jackson held San Francisco hitless until Conor Gillaspie's three-run homer with one out in the seventh inning, and the Padres held off the Giants 5-3 on Sunday for their first sweep of the season. They beat Johnny Cueto, who also was the losing pitcher in the All-Star Game at Petco Park on Tuesday night.
Jackson, making his first start since 2014, and three relievers combined on a two-hitter against the Giants, who despite losing three straight still have the best record in the majors at 57-36.
"It's great to be here," said Jackson, who's with his 11th big league team. "Somewhat of an interesting day to say the least. ... It was definitely a good way to have everything kicked off with a new team. I've been through a lot of ups and a lot of downs. I believe in what I can do. I've always believed in what I can do. It's just a matter of going out and proving it once you get in between the lines."
After striking out Brandon Crawford to open the seventh, Jackson bobbled Gregor Blanco's grounder for an error and then walked Ramiro Pena before Gillaspie homered deep into the seats in right field on a 3-1 fastball. That cut the Padres' lead to 4-3.
"It felt good," Gillaspie said. "I wish we could have mustered a few more runs there at the end. All you can do is compete and give it everything you've got."
Jackson (1-1) was then pulled. He walked five, struck out four and threw 90 pitches.
Until the homer, the Giants hadn't come close to a hit as Jackson kept them off-balance, mostly with his slider.
San Diego remains the only big league team without a no-hitter.
Jackson pitched a no-hitter in 2010 for Arizona, walking eight and throwing 149 pitches to stop Tampa Bay.
The 32-year-old was signed to a minor league deal by the Padres on June 20 after being cut by Miami. He was promoted from Triple-A earlier Sunday to start in place of All-Star Drew Pomeranz, who was traded to Boston on Thursday. San Diego is his 11th big league club.
"I wish he could've picked up that ground ball," manager Andy Green said. "I walked by him, he was in the video room watching it. I was like, 'You're gonna have a hard time letting that one go aren't you?' He was outstanding. Good mix. Slider was really good, mixed in the curveball later on.
"By the end of it he was like gassed. He gave us everything he had and he was outstanding."
Padres catcher Christian Bethancourt worked with Jackson in Atlanta last year.
"He was aggressive. He was attacking the strike zone," Bethancourt said. "I haven't seen that Edwin Jackson in a long time, and I'm so glad I saw it today. I know he will keep doing it and he'll help us win more ballgames."
Jackson hit two singles and drove in a run. He also reached on a fielding error by Crawford.
Brandon Maurer pitched the ninth for his third save.
"We just couldn't mount anything offensively until it looked like he tired out there," Giants manager Bruce Bochy said.
Cueto (13-2) lost for the first time since April 21 against Arizona. He had three straight complete-game victories against the Padres this season coming into Sunday.
Cueto had the same fate as he did in the All-Star Game, when he started for the NL and surrendered two home runs in an inning.
On Tuesday night, he allowed home runs to Kansas City's Eric Hosmer and Salvador Perez in the second.
On Sunday, Cueto allowed a solo homer by Matt Kemp to left-center leading off the fourth and a solo homer by Bethancourt into the first row in the second deck in left with two outs for a 2-0 San Diego lead. It was Kemp's 18th and Bethancourt's fifth.
Cueto made it into the sixth, allowing a leadoff walk to Alex Dickerson and a single to Bethancourt before making way for George Kontos. Rookie Ryan Schimpf hit an RBI single and Jackson followed two batters later with an RBI hit.
Cueto allowed four runs and six hits in five-plus innings, struck out four and walked three.
San Diego's Yangervis Solarte homered in the seventh, his ninth.
Giants: Bochy said OF Hunter Pence, on the disabled list with a strained right hamstring, took Sunday off during his rehab assignment after getting hit by a pitch on Saturday.
Giants: After a day off, San Francisco opens a two-game series at Boston on Tuesday night when RHP Jake Peavy (5-7, 5.09) is scheduled to oppose RHP Rick Porcello (11-2, 3.66). Peavy started three postseason games for the Red Sox during their 2013 run to the World Series title.
Padres: San Diego heads to St. Louis for a four-game series starting Monday night, when LHP Christian Friedrich (4-5, 4.50) is set to face RHP Mike Leake (6-7, 4.14), who grew up in San Diego County.