Raburn, coming off back-to-back two-homer games, drove in two runs with a single in the third and a double in the fifth. He has 12 hits in his last 14 at-bats, a stretch that began Sunday, while totaling four homers, nine RBIs and five runs scored in the last four games.
The Indians have won a season-high four straight games in which they have outscored their opponents 39-5.
Bauer (1-1), called up from Triple-A Columbus before the game, walked six while striking out five and combined with four relievers for the shutout.
Cliff Lee, pitching against the Indians for the first time since Cleveland dealt him to Philadelphia during the 2009 season, allowed five runs in six innings. Lee (2-2) has given up 13 runs and 26 hits in 18 innings in his last three starts.
Raburn, who was 2 for 19 with seven strikeouts in his career against Lee coming in, singled in the second when the Indians took a 1-0 lead on Mike Aviles' sacrifice fly. Raburn's infield hit in the third capped Cleveland's three-run rally and his RBI double in the fifth gave the Indians a five-run lead. He added a bloop single in the seventh off Jeremy Horst. While fans were chanting his name in the eighth inning, Raburn struck out against Phillippe Aumont.
Raburn has taken advantage of increased playing time due to injuries to Nick Swisher and Michael Bourn. Over his last seven games, Raburn is batting .500 (15 for 30).
Asdrubal Cabrera had a two-run double in the third while Michael Brantley had three hits.
Bauer was likely making a spot start as the Indians needed an extra starter because of a rainout last week. The right-hander, who walked seven in five innings in his first start against Tampa Bay on April 6, didn't allow a hit until Domonic Brown's two-out single in the fourth. Raburn took an extra base hit away from Ryan Howard with a catch at the wall in right field earlier in the inning.
Bauer walked the first two hitters in the fifth, but retired Jimmy Rollins, Michael Young and Chase Utley to end the inning.
Cleveland was the only team Lee hadn't faced in his career. Lee won the AL Cy Young Award with the Indians in 2008, going 22-3 with a 2.54 ERA. Cleveland also defeated Roy Halladay, another former Cy Young winner, on Tuesday.
The Indians' third-inning rally was keyed by three infield hits. The inning began on a bunt hit by Brantley, followed by a walk to Jason Kipnis. Cabrera doubled past third base to score both runners. Mark Reynolds' hit to deep shortstop moved Cabrera to third. After Carlos Santana struck out, Raburn hit a slow roller that third baseman Michael Young had no play on and Cabrera scored.
Lee got a boost from his defense when right fielder Laynce Nix robbed Drew Stubbs of a home run with a leaping catch at the wall in the fourth.
Swisher missed his second straight game because of a sore left shoulder.
Delmon Young started at designated hitter for the second straight game for the Phillies. Manager Charlie Manuel planned on playing Young in right field, but he was struck on his throwing elbow by a pitch from Zach McAllister on Tuesday. Making his season debut in that game, Young homered in his first-bat.
NOTES: Phillies OF Ben Revere had a seventh-inning single, but remains in a 4-for-28 slump. On the season, he is batting .204 with one extra-base hit and five walks in 100 plate appearances. ... Manuel said Delmon Young will be limited to pinch-hitting when the Phillies open a four-game series at home against Miami on Thursday. ... Cabrera, the Indians' everyday shortstop, was the DH while Aviles started at short. ... OF Michael Bourn (lacerated finger) remains sidelined and there's no timetable for his return. ... RHP Brett Myers (sore elbow) will be re-evaluated during the weekend and could be cleared to begin a throwing program. ... The Indians made room for Bauer on their 25-man roster by optioning LHP Nick Hagadone to Triple-A Columbus. Hagadone went 0-0 with a 2.45 ERA in eight relief appearances.
