McCutchen hit a 2-2 pitch from Mike Fiers (0-2) into the right-center field stands for his fifth home run of the season and the fourth game-ending shot of his career.
Pittsburgh's Jose Tabata had three hits, Russell Martin hit two doubles and Neil Walker had two hits.
Vin Mazzaro (2-0) pitched two scoreless innings to help the Pirates beat the Brewers for the just the second time in their last 12 meetings. Milwaukee had won five straight games at PNC Park.
Ryan Braun had three hits, including a pair of doubles, for the Brewers after sitting out Monday night's win over the Pirates with stiffness in his neck and upper back. He also made a diving catch to rob John McDonald of extra bases leading off the 11th inning.
Norichika Aoki also had three hits for Milwaukee, Carlos Gomez added two hits and Jean Segura drove in two runs.
Milwaukee starter Kyle Lohse did not receive a decision after losing his previous three starts. He gave up three runs, five hits and five walks in 5 2-3 innings while striking out three.
Lohse is 1-4 in eight starts after signing a three-year, $33-million contract late in spring training as a free agent. The Brewers have scored only 15 total runs in his eight starts.
Jeff Locke, who has won his last three decisions for the Pirates, pitched six innings and allowed three runs on seven hits with one walk and six strikeouts.
Pittsburgh had a chance to win the game in the bottom of the ninth when Tabata doubled with one out and McCutchen was intentionally walked. However, Alfredo Figardo induced Garrett Jones to ground into an inning-ending double play.
Pittsburgh tied the game at 3-3 in the eighth inning on Martin's run-scoring double off John Axford. Walker led off the inning with a looping single to left field and then scored all the way from first with one out when Martin doubled into the left-field corner.
Walker also scored in the sixth to get the Pirates within a run. He walked, moved to third on Martin's first double of the game and scored on Clint Barmes' groundout.
Braun hit a leadoff double in the fourth and scored on Gomez's one-out double to break a 1-1 tie. In the fifth, Aoki lined a single off Locke's leg with one out, advanced to third on a pair of wild pitches and scored on Segura's groundout.
Segura opened the scoring with his seventh home run of the season in the top of the first inning.
The Pirates tied it at 1-1 in the bottom half when Starling Marte led off with a single and scored on Jones' groundout.
NOTES: Home plate umpire Fieldin Culbreth was forced to leave the game in the top of the 11th inning when he was struck in the collarbone by a foul ball off the bat of Milwaukee 1B Yuniesky Betancourt. Second base umpire Bill Welke took over behind the plate. . Brewers 2B Rickie Weeks returned to the lineup after being limited to pinch-hitting duty Monday as manager Ron Roenicke wanted to give him a mental break. Weeks had started every game this season . Martin started for Pittsburgh after missing four consecutive games and six of the last seven because of a stick neck. . The Pirates were the last team in the majors that had not played an extra-inning game this season. . Yovani Gallardo (3-2, 4.70 ERA) will pitch Wednesday night for Milwaukee against left-hander Wandy Rodriguez (3-2, 3.62).