Paulino, making his second start, cruised through the first four innings, yielding three hits and benefiting from a pinpoint throw from Hunter Pence to Humberto Quintero to prevent Mike Cameron from scoring in the fourth. Cameron pummeled Quintero at the plate, but the catcher hung onto the ball to record the out.
Lee knocked a two-run homer off Yovani Gallardo in the bottom of that frame, putting the Astros ahead, 2-0. But the Brewers logged six singles in the next inning, generating four runs.
At several points that inning, Paulino appeared to be in control. He put several hitters behind with 0-2 counts, but he could not seem to finish the job.
He had Jason Kendall down, 0-2, but Kendall knocked a base hit to end a seven-pitch at-bat. Gallardo sacrificed him to second, and Rickie Weeks reached on an infield single, pushing Kendall to third.
Paulino then threw two sliders for strikes to Corey Hart, but he followed that with a 97-mph fastball, up in the zone, that Hart whacked to right field for an RBI single.
"I was supposed to throw inside, a sinker," Paulino said. "But the ball stayed right down the middle."
Ryan Braun knocked a 1-1 slider to right field for a base hit, and Prince Fielder followed with a single to the same spot on a 1-0 changeup. Cameron singled on an 0-1 fastball to drive in the fourth and final run of the inning.
"It was a semi-good pitching performance," Cooper said. "That fifth inning wasn't very good. There were some 0-2 pitches there that could have been a little bit better. I thought the first four [innings] were pretty good, though. We have to figure out a way to get some hits and score some runs."
Said Paulino: "After I had two outs, I made mistakes. I put the hitters behind the count, but rather than put the ball into play, I made a mistake. I left the ball up."
Gallardo, meanwhile, continued his dominance over the Astros. After Lee's home run, the Astros barely made a peep, logging just two more hits.
Gallardo is now 3-0 against Houston with an 0.75 ERA over three career starts. Until Lee's home run, he had shut out the Astros for 18 1/3 consecutive innings. The complete game was the first of his career.
"His stuff was very crisp," Milwaukee manager Ken Macha said. "He had some help [defensively] getting out of that first inning. Except for one [pitch], he was in control. The biggest benefit [of a complete game] was for Yovani. He knows he can go out there and go nine. We've put together maybe seven out of eight quality starts, and we're starting to swing the bats a little."
The Astros are 3-5 so far in this 10-game homestand. They lost three of four to the Reds, took two of three from the Dodgers and are now in an 0-1 hole against the Brewers.
The offense continues to be a problem. The Astros entered the game hitting .229 during the homestand, as opposed to .279 by opponents.
"You look around, and we're way better than this," Lee said. "We're a better team than that is showing up right now. I hope it turns around soon."