The win came after the teams waited out a 2-hour, 41-minute rain delay, and a ninth-inning comeback by the Cubs.
Darwin Barney led off the 11th with a double. Wellington Castillo was intentionally walked and pinch-hitter Jeff Samardzija was hit by a pitch to load the bases. On a 3-2 pitch, DeJesus drew the game-winning walk.
With the Cubs trailing 3-2 in the bottom of the ninth, pinch-hitter Ian Stewart singled, and Dodgers closer Javy Guerra walked David DeJesus. Tony Campana hit a tying double, but DeJesus, who would have been the winning run, was thrown out at home.
It was Guerra's third blown save in 11 chances. Rafael Dolis (2-2) got the win, while Jamey Wright (1-2) took the loss.
Dodgers slugging center fielder Matt Kemp was a late scratch due to tightness in his left hamstring. He pinch hit in the seventh inning and flew out to right field.
The Dodgers were in position early to win, thanks to Juan Rivera's two-run homer in the third inning and a quality start from Aaron Harang. Rivera's second homer of the year into the left-field bleachers gave the Dodgers a 3-0 lead that held up - until the ninth.
Harang posted his best start of the season, going six innings and allowing two runs. He outdueled the Cubs' Travis Wood, who allowed three runs in six innings in his first start of the season. Wood was called up from Triple-A Iowa to fill in for Matt Garza, who was suffering from the flu.
The Dodgers scored first in the second inning. Jerry Hairston reached on an infield single and A.J. Ellis and Tony Gwynn Jr. drew back-to-back walks, before Harang drove in a run on a forceout.
The Cubs cut the lead to 3-2 in the bottom of the third when Wood led off with a double, DeJesus walked and Starlin Castro hit a two-out, two-run single.
The Cubs had chances to tie it before the ninth, but could not deliver a clutch two-out hit. Chicago left runners in scoring position in the fifth, sixth, seventh, and eighth - twice by Castro.
The bullpens combined to allow two runs in nine-plus innings. The Cubs bullpen allowed just three hits in five innings.
Cubs first baseman Bryan LaHair continued his torrid start to the season, going 3 for 4 and raising his batting average to .390.
Notes: The Cubs designated Blake DeWitt for assignment before the game to make room for Wood. ... Dodgers INF Juan Uribe did not start for the fifth straight game with a sore left wrist. ... The Cubs host Atlanta on Monday with Samardzija taking on Tommy Hanson. Meanwhile, the Dodgers return home to play San Francisco with Ted Lilly opposing Barry Zito.