Rollins' bases-loaded blast in the second was his 200th career home run and highlighted a six-run frame for the Phillies, who pounded out 17 hits and racked up their most runs on Opening Day since posting a 19-17 victory over the Boston Beaneaters on Opening Day, 1900.
Ben Revere went 3-for-6 with three RBI and two runs scored, while Asche and John Mayberry each drove in two runs in the victory. Philadelphia starter Cliff Lee (1-0) picked up the win despite being hammered for eight runs on 11 hits over five frames.
Alex Rios stroked a three-run homer among his three hits and scored three times, while Josh Wilson went 2-for-3 with three RBI for the Rangers, who went 91-72 last season, but missed out on the postseason for the first time in four years.
Texas first baseman Prince Fielder, who the team acquired for second baseman Ian Kinsler in a blockbuster trade with the Detroit Tigers over the winter, finished 1-for-5 with a run scored in the setback.
Tanner Scheppers made his first career start for the Rangers, but was shelled for seven runs on eight hits over four frames. Pedro Figueroa (0-1) was pegged with the loss after giving up four runs on four hits in 1 2/3 frames.