Edwin Encarnacion hit a solo homer and tripled for two of Cincinnati's four hits. Rookie sensation Jay Bruce had a checked-swing, infield single in three at-bats.
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.
Griffey hit No. 599 at home Saturday against Atlanta. The only players to reach 600 are Barry Bonds, Hank Aaron, Babe Ruth, Willie Mays and Sammy Sosa.
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.
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.
J.C. Romero and Gordon combined for four outs, and Brad Lidge finished for his 15th save in as many chances. Lidge retired Encarnacion on a shallow fly with two runners on to end it.
The NL East-leading Phillies have won eight of nine.
Chase Utley led off Philadelphia's sixth with a double. After Ryan Howard struck out, Burrell hit a towering drive into the left-field seats to give the Phillies a 3-1 lead.
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.
Notes: 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.
