Sheets pitched seven innings, giving up one run and retiring the final 14 batters he faced.
"Well, the results were terrible for the team, but I got deep into the game and threw strikes," Sheets said. "The shoulder feels good and felt good -- better than I anticipated."
Bush (6-8) relieved him and allowed five runs in the eighth.
"I felt fine, warmed up fine and felt good, just didn't make the pitches in critical situations," Bush said.
Ian Snell (9-6) matched Sheets, yielding one run and four hits in seven innings for the Pirates. He struck out nine and walked one.
"Seven terrific innings of pitching," Pittsburgh manager Jim Tracy said. "Really great pitching on both sides of the field."
Snell departed when a bruise he suffered on his left foot in the fifth inning started to hurt. He said he would be OK for his next start.
"The later the innings, it all started falling into place," Snell said. "I kept throwing harder and harder, and the breaking ball was even better."
Burnitz homered against Sheets in the second to give Pittsburgh a 1-0 lead, but Prince Fielder hit a drive off Snell in the fifth to tie it. It was Fielder's 18th homer of the season.
Sheets left after seven and the Pirates jumped all over Bush. Nate McLouth hit a leadoff single and Jack Wilson bunted for a sacrifice, but Bush's throw to first was wild for an error, allowing the runners to advance to second and third.
In his last four appearances, Bush has given up 15 earned runs in 12 innings. The team's No. 5 starter, he has pitched out of the bullpen twice this month because the team has had days off and did not need him to start.
"I don't think it matters a whole lot," Bush said of relieving. "I've relieved for a lot of years early on in my career and in college. It shouldn't make a difference."
Sheets' outing still gave the Brewers plenty of reasons for hope, despite the loss. The right-hander, out since May 3 with tendinitis in his pitching shoulder, gave up six hits, struck out five and didn't walk a batter.
"I just had to get in a groove, and started having a little fun," Sheets said.
The Brewers believe they can make a run at the NL wild card with Sheets and right-hander Tomo Ohka back in the rotation. Both pitchers missed nearly three months while injured, and the team went 6-17 in games started by their replacements.
Ohka has made two starts this month, giving up only three earned runs in 13 innings.
Fielder's home run set the Brewers' rookie record. The previous record of 17 was held by Danny Walton in 1970 and Greg Vaughn in 1990. ... Before the game, the Brewers acquired infielder Tony Graffanino from Kansas City for left-hander Jorge De La Rosa.
Graffanino is expected to be in Milwaukee for the Brewers' Wednesday afternoon game against Pittsburgh. After the game, the team optioned INF Chris Barnwell to Triple-A Nashville to make room for Graffanino. ... Pirates LF Jason Bay struck out in the sixth to snap a streak of eight plate appearances in which he reached base. ... It was only Pittsburgh's fourth road victory in its last 19 games.