Eveland (2-0) threw 63 of his 94 pitches for strikes, and gave up only three hits while fanning three and walking two. He gave up only one run over eight frames in his first outing of the season on September 1 against the Pirates.
Kenley Jansen finished a scoreless eighth and Javy Guerra shut down the Giants in the ninth to notch his 18th save of the season.
"We've been playing well lately," Guerra said. "We're going to try to keep it up."
Brett Pill clubbed a double for the Giants, who have lost three straight and eight of 12.
Ryan Vogelsong (10-7) was saddled with the loss, surrendering three runs on nine hits over eight full frames while fanning six and walking one.
Los Angeles opened the scoring in the second inning when Loney ripped a one- out triple to right and scored on a groundout by Jerry Sands to give the Dodgers an early lead. They made it stand up.
The Dodgers extended their lead in the fourth when Kemp smoked a triple into the right field corner to begin the frame and came around to score on a single by Rivera to make it a 2-0 game. Loney and Sands both reached on infield singles to load the bases with no outs. The Dodgers were gifted a run when Vogelsong was called for a balk, which allowed Rivera to waltz home with the Dodgers' third run. Vogelsong battled back to limit the damage, getting A.J. Ellis to ground into a fielder' choice, inducing a pop out from Jamey Carroll and striking out Eveland.
After not threatening all game, San Francisco finally mounted a threat in the eighth. Hector Sanchez coaxed a walk from Eveland to begin the frame and Dodgers manager Don Mattingly elected to pull Eveland and go with his set-up man Jansen. Pinch-hitter Mark DeRosa ripped a single to put runners on the corners with no outs. The Giants were unable to capitalize though, as Jansen fanned pinch-hitter Aubrey Huff and Jeff Keppinger for the first two outs, and got Carlos Beltran to ground out to second to preserve the shutout for his team.
"We were really bad with the bat tonight," Giants manager Bruce Bochy said. "We were awful."
The Giants got the tying run to the plate in the ninth. Pablo Sandoval walked to begin the frame, moved to second on defensive indifference and went to third on a single by Orlando Cabrera. Cabrera then moved to second to give the Giants runners on second and third with two down. Pinch-hitter Pat Burrell struck out to end the game.
San Francisco has scored two or fewer runs in 65 of its games this season...The season series between the teams is tied at seven games apiece...The Dodgers are 32-27 against the National League West, while the Giants are 32-23 against the N. L. West...The Giants left eight men on base, while Los Angeles left 10.