SAN DIEGO -- Edwin Jackson made quite a first impression on the San Diego Padres.

"It's definitely a great way to kick off being with a new team," Jackson said.

Jackson was solid in his Padres debut as San Diego defeated the National League West-leading San Francisco Giants 5-3 on Sunday afternoon at Petco Park.

Jackson (1-1), making his first start since 2014 with the Chicago Cubs, had a no-hitter through 6 1/3 innings. He was aiming to throw his second career no-hitter and the first in Padres history, a span of 7,582 games.

"It was an interesting day, to say the least," Jackson said.

The veteran right-hander surrendered three runs (two earned) and one hit as the Padres notched their first three-game sweep of the season. Jackson walked five and struck out four, mostly mixing his fastball, which reached the mid-90s, with a biting slider and curveball.

Jackson was chased after getting dinged by Conor Gillaspie's three-run, pinch-hit home run in the seventh inning, pulling the Giants to within 4-3. Gillaspie crushed the 3-1 cut fastball 404 feet, driving in Gregor Blanco, who reached on a fielding error by Jackson, and Ramiro Pena, aboard on a walk.

"It was that half-second I took my eye off the ball," Jackson said about Blanco's two-hopper to the right of the mound that he booted. "If I make that play, maybe things go differently."

Brandon Maurer pitched the ninth for his third save.

All-Star Game starter Johnny Cueto (13-2) took his first loss since April 21 for San Francisco. He was charged with four runs and six hits in six innings as he struck out four and walked three.

"I went out there and forgot about how bad I felt," Cueto said through a translator. "I tried to do the best I could but I had a bad day."

Added Giants manager Bruce Bochy about Cueto being under the weather: "He wasn't at full strength."

Cueto had three complete wins against the Padres before Sunday.

"We talked about that before the game," said catcher Christian Betancourt, who caught Jackson last year with the Atlanta Braves. "We were kind of mad at him about that."

After Gillaspie's blast, the Giants had the go-ahead run aboard when reliever Brad Hand issued consecutive one-out walks to pinch-hitter Mac Williamson and Denard Span. But Hand got Angel Pagan to fly out and Brandon Belt struck out.

Yangervis Solarte's ninth homer in the seventh game the Padres' their final run.

The Padres padded their lead to 4-0 in the sixth. Ryan Schimpf had an RBI single and Jackson collected one as well, his second hit of the game.

That was one more than he gave up.

"He was great," Padres manager Andy Green said. "He was exactly what we needed."

Jackson said he's eager to prove he's not done.

"My career has had a lot of ups and downs but I believe in what I can do," Jackson said. "I know I still have life in my arm and I still feel like I can bring a lot to the table, that I have a lot to offer."

NOTES: Giants manager Bruce Bochy said RHP Matt Cain (hamstring) will start on Wednesday against the Red Sox. ... San Francisco 3B Matt Duffy (Achilles) will go the team's facility to begin a running program. ... Padres RHP Edwin Jackson was called up from Triple-A El Paso to start Sunday's contest. LHP Buddy Baumann was optioned to El Paso. ... San Diego C Derek Norris was not in the starting lineup.