Escobar's third-inning homer gave the Braves the 4-0 lead over Lincecum, who lost for the first time in five weeks.
Jurrjens (9-7) earned his third straight win and set a season high with nine strikeouts while allowing one run.
Jurrjens lowered his ERA to 2.67, not far behind Lincecum's 2.45 among the NL leaders. But the Braves scored only five runs for Jurrjens in his four-game losing streak in June.
"We have probably not done right by J.J. all year long, so it's always very gratifying when he's throwing that good to give him a little breathing room," Escobar said through his interpreter, Braves coach Chino Cadahia. "And we knew tonight facing Lincecum it was going to be a low-scoring affair."
The Braves are 6-1 since the All-Star break and are 10-3 in their last 13 games overall.
"It's a nice start for us and we gained ground tonight and that's what we have to do," manager Bobby Cox said, referring to first-place Philadelphia's 10-5 loss to Chicago. "Gain a game here and there, see what happens."
Lincecum (10-3), the NL's All-Star starter, lost for the first time since June 17 and for the first time in six career starts against the Braves.
Jurrjens said he was motivated by the matchup against the 2008 NL Cy Young winner.
"Every time you face an ace from a team you put a little pressure on yourself," Jurrjens said. "You know if they score a couple of runs, maybe that's the game."
"He's one of the best pitchers in the league and probably the Braves' best pitcher," Bochy said.
The Giants are 1-5 on their 10-game trip, including three straight losses to the Braves. Overall, they have lost six of seven.
"It's a matter of bouncing back and putting the last few games behind us," Lincecum said.
Lincecum pitched five innings, his second-shortest start of the season, allowing four runs and seven hits with nine strikeouts.
"All my pitches were up," Lincecum said. "I probably was just rushing. I usually take time to get my rhythm. I was kind of fighting it to get my pitches down."
Jurrjens, who has allowed a combined five hits and one run in his last two starts, said he was also focused on his pace.
"In my last couple bullpens I feel like I've been rushing too much," he said. "I've been trying to find something to stay on the rubber to have more control of all my pitches. We found something in the last bullpen and I did it today in the game and it helped me out."
Jurrjens gave up a second-inning single to Bengie Molina and didn't allow another hit until Molina's two-out single in the seventh. Jurrjens left with two outs in the eighth after giving up Juan Uribe's double and a walk to pinch-hitter Andres Torres.
Rafael Soriano allowed a run in the ninth before earning his 14th save. With two outs, Nate Schierholtz singled, took second base without a throw and scored on Travis Ishikawa's single to right. Soriano struck out Uribe to end the game.
Lincecum struck out seven in the first three innings but still gave up four runs in that span.
Martin Prado singled in the third before Lincecum walked Anderson and gave up Escobar's three-run homer to center. The homer was Escobar's 10th, matching last season's career high.
Escobar has three homers and 12 RBIs in seven games since the All-Star break.
Giants SS Edgar Renteria was held out with a sore right elbow. ... Giants CF Aaron Rowand (bruised right forearm) missed his second straight start and grounded out as a pinch-hitter in the eighth. ... Casey Kotchman extended his career-best hitting streak to 14 games. ... Jurrjens' career high for strikeouts was 10 on Sept. 11, 2008, against Colorado.