Marquis (7-2) allowed two runs and three hits in 6 1/3 innings while improving to 6-0 with a 3.28 ERA in his past eight starts. The veteran right-hander also is 3-0 with a 2.52 ERA in his past four outings against the Dodgers dating to last season.
"He gives us trouble all the time," Dodgers manager Don Mattingly said. "Ever since I've been out here in California, it seems like he pitches good every time."
Marquis had his no-hitter broken up when Skip Schumaker doubled to deep center field with two outs in the sixth, extending his hitting streak to 12 games. Adrian Gonzalez followed with an RBI single that trimmed San Diego's lead to 3-1.
Earlier in the inning, Padres right fielder Kyle Blanks temporarily preserved Marquis' no-hit bid with a diving catch and slide on his belly that robbed pinch hitter Jerry Hairston Jr.
"Outstanding," Marquis said.
Marquis left after Scott Van Slyke homered with one out in the seventh. He struck out six and walked two.
"I saw the legit sinker just pounding it on right-handers and keeping it away from lefties," Padres manager Bud Black said. "It was a lot of sinkers and good sliders down underneath."
Dodgers ace Clayton Kershaw (5-4) struck out nine, and was charged with three runs and seven hits. The left-hander gave up at least one hit in each of his six innings.
"I saw a lot of tough at-bats against a very good pitcher," Black said.
The last-place Dodgers could have passed the Padres in the NL West standings with a victory, but they never led while falling to .500 at home with a 16-16 record.
Gyorko also had a leadoff homer in the fourth, and walked and scored on Jesus Guzman's double in the sixth. Guzman tied his career high with three hits.
"They're a scrappy team. They've got a lot of grit over there," Kershaw said. "They're fouling pitches off and putting good at-bats every single time out there. You've got to tip your cap to them. They're not going to be easy outs."
The Padres grabbed the lead on Grandal's RBI single with two outs in the second. Dodgers rookie Yasiel Puig went to field the ball with his left-handed glove and it went behind him, allowing Guzman to score.
Puig was hitless in four at-bats with two strikeouts after going 5-for-8 in his first two major league games Monday and Tuesday, when he had two homers and five RBIs.
"Marquis is a tough matchup," Mattingly said. "He's a guy who keeps the ball down, he can run the ball at him and break the ball to the other side."
Dodgers LHP Scott Elbert will undergo Tommy John surgery next week and is expected to be out 12 to 16 months. ... Dodgers RHP Josh Beckett is confident he will pitch again this season, although he won't throw for another four weeks. Currently on the disabled list with a left groin strain, Beckett has been diagnosed with irritation of an upper arm nerve that causes numbness in his right hand and fingers. ... Marquis hasn't lost since April 22, a 7-1 defeat to Milwaukee. ... The Padres announced after the game they will reinstate OF Cameron Maybin from the disabled list Thursday and option Blanks to Triple-A.
The Associated Press contributed to this report.
Copyright by STATS LLC and The Associated Press
LOS ANGELES, CA - JUNE 05: Clayton Kershaw #22 of the Los Angeles Dodgers throws a pitch against the San Diego...