Billingsley (0-1) walked seven and gave up seven hits in 5 2/3 innings en route to surrendering six earned runs. The right-hander threw 103 pitches, just 55 for strikes.
"That's not nearly good enough," manager Grady Little said. "He had to pay for it tonight.
"He couldn't get anything working for him."
Billingsley allowed four runs in the first two innings, and was credited with two more after he exited with two outs in the sixth inning when reliever Hong-Chih Kuo allowed consecutive RBI singles.
Minnesota's Joe Mauer hit an RBI single with nobody out as the first three Twins reached base in the first. In the second, Mauer tripled down the line when left fielder Andre Ethier lost the ball in the dome's lights, driving in a pair of runs to give Minnesota a 4-1 lead.
Billingsley threw 53 pitches in the first two innings, walking four and hitting one batter. But he loosened up and starting throwing more fastballs, and combined for just 18 pitches in the third and fourth innings.
"I was just trying to pick my way around the plate and trying to hit too much corners, instead of just going right after them and pounding the zone," Billingsley said. "It's part of the learning process.
"Pitchers, you find, give the hitters too much credit instead of trusting ourselves and our abilities to have the hitters get themselves out. That's the adjustment I made going into the third inning -- going right after them, and trust yourself."
And Billingsley admitted his outing could have been worse.
Minnesota's Torii Hunter narrowly missed a grand slam in the first inning with a foul blast down the left-field line, and then grounded into an inning-ending double play. The next inning, Billingsley got Justin Morneau to ground out with runners on the corners.
In the fifth inning, Ethier caught a fly ball and threw out Michael Cuddyer, who tried to tag up and score at home, for the final two outs.
"I'll tell you what, to get through the first two innings like he did, and hang in there and battle and get us into that sixth inning was something we liked to see," Little said. "But he had a little rough start there."
Twins starter Carlos Silva (4-8) threw eight innings and allowed just six hits -- four of which came in the second and third innings. He didn't walk a batter, struck out six and forced 16 flyouts.
Designated hitter J.D. Drew doubled to lead off the second inning. He scored two batters later when Ethier hit a sacrifice fly to right field. In the third inning, Rafael Furcal singled and stole second base. Nomar Garciaparra singled to drive in Furcal, who had two hits.
The Dodgers notched just two more singles off Silva and didn't advance a runner into scoring position.
"[Silva] changed speeds really well thoughout the game," Little said.
Garciaparra went 2-for-4 with a pair of singles and leads the National League with a .364 batting average.