"We're on a good roll now," Burrell said after the NL East leaders won for the eighth time in nine games. "We want to keep it going."
Griffey walked as a pinch-hitter in the eighth inning to remain one shy of 600 home runs. Griffey wasn't in the Reds' lineup for the second straight game because of general soreness. He's been bothered by a sore left knee, though he could return Wednesday.
Junior represented the tying run when he came up with one out, but walked on four pitches and pitcher Bronson Arroyo ran for him. A sellout crowd gave Griffey a standing ovation and booed when reliever Tom Gordon didn't throw a strike.
"We didn't want him to hit one," Phillies manager Charlie Manuel said. "The tension was there. The excitement was there. You could tell. You could feel it. It's good for the game. We definitely didn't want him to tie the game up."
The Reds lost center fielder Ryan Freel to a strained right hamstring in the sixth. Freel crumbled to the ground after taking several steps out of the batter's box following a grounder to shortstop. Freel quickly hopped up and hobbled off the field on his own. He'll fly to Cincinnati on Wednesday for further evaluation.
"He said he heard something pop," Reds manager Dusty Baker said. "That was just bad luck."
Eaton (2-3) allowed one run and three hits, outpitching Aaron Harang (2-8). Eaton has won consecutive starts after going winless in his first 10.
A constant target for boos because he's pitched poorly after signing a free-agent contract before last season, Eaton left to a standing ovation, and tipped his hat to the crowd.
"I think it was the best stuff I've had," Eaton said.
Harang gave up three runs and nine hits in six-plus innings. He didn't get any run support again -- the Reds have scored 16 runs in his eight losses.
"We're not scoring for Aaron," Baker said. "He made one mistake to Pat and lost it."
"I feel the only mistake I made was the hanging slider to Burrell," Harang said. "If I make a good pitch instead of hanging it, I probably get him swinging."
Encarnacion tripled to start the eighth off Gordon. Pinch-hitter Javier Valentin's sacrifice fly cut it to 3-2, but Gordon got out of the inning after walking Griffey.
Encarnacion hit a solo shot leading off the third to give the Reds a 1-0 lead. Eaton had retired the first six batters before Encarnacion lined his 10th homer into the left-field seats.
Utley had a broken-bat RBI single with two outs in the third to tie it at 1. Utley, who leads the majors with 21 homers, didn't hit one out for the first time in six games.
Before getting hurt, Freel made a sensational play to save a run in the fifth. With two outs and a runner on third, Freel made a headfirst, diving catch on a sinking liner by Shane Victorino.
Harang left after pinch-hitter Greg Dobbs singled and Jimmy Rollins doubled to start the Phillies' seventh. Left-hander Danny Herrera entered for his big league debut and retired Victorino on a grounder to shortstop. After Utley was intentionally walked, Herrera fanned Howard and Burrell to escape the jam.
"I was very impressed with him," Baker said. "He wasn't scared."
Rollins stole his 23rd and 24th consecutive bases, dating to last season. It's the longest streak in the majors. ... Victorino was 0-for-3 with a walk, snapping his 14-game hitting streak. ... Dobbs leads the majors with 14 hits as a pinch-hitter. ... Cincinnati's Jerry Hairston was 0-for-4, ending his 10-game hitting streak. ... The Reds have lost 14 of 17 on the road.