Nelson took a no-hitter into the sixth inning before it was broken up when pinch hitter Chase Utley singled with one out. He allowed two runs on four hits in 6 2/3 innings, striking out six and walking two.
"Jimmy was really good," Brewers manager Craig Counsell said. "He pitched beautifully. No hits through five innings. We probably should've escaped with just giving up one run. He pitched beautifully."
The Dodgers, who own the best record in baseball at 91-38, hadn't lost consecutive games since July 20-21.
Darvish, who landed on the DL with a sore back, threw 95 pitches and worked to get out of several jams. He was done after striking out seven and walking three.
"The overall stuff was really good and the fastball had life," Dodgers manager Dave Roberts said. "I think in talking to Yu and talking to (pitching coach) Rick (Honeycutt), there was a mechanical adjustment he's been working through over the last 10 days with his bullpens. To take it from a bullpen to a game, obviously things speed up.
"He was trying to find a rhythm and some consistency. Toward the end of the game, he felt more comfortable and slowed the game down a little bit."