Randy Wolf (3-1) yielded one run and four hits in 7 2/3 innings for the Phillies, who had lost four of five before the three-game series. The Phillies also swept the Rockies at Veterans Stadium last May and have beaten them seven straight meetings here.
Philadelphia had a 2-0 lead when Utley sent a pitch from Aaron Cook just over the wall in right field. Utley, a second baseman who was recalled from Class AAA Scranton prior to the game, struck out as a pinch-hitter against Pittsburgh on April 4 and flied out in the second inning Thursday.
The last Philadelphia player to record a grand slam for his first hit was Jim Command against the Brooklyn Dodgers on July 11, 1954.
The six-run cushion was more than enough for Wolf, who surrendered just a one-out solo homer to Jay Payton in the fourth inning after retiring his first 10 batters.
The starter pitched himself out of bases-loaded jams in the next two frames, getting a strikeout and two popouts with nobody out in the fifth and inducing Gabe Kapler to hit into a double-play to end the sixth.
The Phillies took a 7-1 lead on a homer by Pat Burrell against Dan Miceli on the first pitch of the bottom of the fifth, then added two runs against Jose Jimenez in the eighth.
Cook (1-2) allowed six runs and six hits in just four innings. On Friday, he pitched a five-hitter in a 12-1 victory over San Diego.