Howard came into the game an RBI behind Prince Fielder, who entered with 131, for the major league lead, but he drove in Chase Utley with two outs in the first and added another in the eighth.
Fielder hit a run-scoring grounder in the bottom of the ninth to tie the sluggers at 132.
Howard, who doubled, homered and drove in four runs on Wednesday night at Florida, now has six RBIs in two games.
Happ (11-4) tied Randy Wells of the Chicago Cubs for the most victories by a rookie as he turned in a much better performance against Milwaukee than his previous start. On Sept. 18 at Atlanta, he went just three innings in the shortest start of his career, leaving for precautionary reasons. He had strained his right oblique during batting practice Sept. 5.
Happ, who missed two starts due to the injury, retired the first seven batters, the last five on strikeouts, before Jason Kendall hit a sinking liner in the third that left fielder Ben Francisco made a diving attempt to catch, but missed. The ball rolled to the wall as Kendall legged out his second triple of the season. One out later, Happ deflected Lopez' smash up the middle toward second where Utley's low throw handcuffed Howard at first and squirted away as the run scored.
Milwaukee starter Jeff Suppan (7-11) immediately gave the run back on consecutive doubles by Francisco and Feliz to start the fourth.
Leading 2-1, the Phillies broke the game open with six runs in the fifth to chase Suppan.
Jayson Werth reached on shortstop Alcides Escobar's throwing error and then four consecutive singles produced three runs, including one by Happ, who drove in his first run, just before Rollins hit his 20th of the season.
Suppan was booed as he walked off the field.
Suppan allowed eight runs - seven earned - and a season-high 12 hits over 4 1-3 innings. He had not faced the Phillies since Game 4 of the NLDS last season at Miller Park, when he gave up five runs on three homers in three innings of the decisive 6-2 loss.
Happ left with an 8-2 lead and two outs in the sixth after the Brewers scored a run on consecutive doubles by Fielder and Casey McGehee. He allowed two runs on six hits in five 2-3 innings with two walks and seven strikeouts.
NOTES: Happ leads all rookies in ERA (2.79), complete games (three), shutouts (two), strikeouts (112) and innings pitched (158 1-3). ... Phillies C Carlos Ruiz was not with the team after being sent home on Wednesday to undergo an MRI on his sprained left wrist. He had a cortisone shot on Thursday in Philadelphia and then left to join his teammates at Miller Park. He is not expected to play for a few days. ... Plastic sheeting was rolled up and hanging above the players' clubhouse lockers in anticipation of the Phillies clinching the NL East during the four-game series with Milwaukee. ... Milwaukee (75-78) is out of the playoff race, but hopes to keep Ken Macha's streak of winning records alive. The Brewers' first-year manager, who led the Oakland Athletics for four years and two teams in the minors for four seasons, has never finished below .500.