Cliff Lee (1-0) matched his career high by allowing eight runs and struck out only one, but the left-hander made it through five innings in another less-than-stellar opener for him in the Rangers' home ballpark.
Marlon Byrd and Cody Asche also homered for the Phillies.
Converted Rangers reliever Tanner Scheppers gave up seven runs over four innings, including the slam by Rollins that made it 6-0 in the second. But the game was tied when Scheppers threw his last pitch.
Mayberry, a first-round draft pick by the Rangers in 2005 who never played for the big league club and was traded three years later, had his tiebreaking hit in the fifth off Pedro Figueroa (0-1) for a 9-7 lead.
With starters Yu Darvish, Matt Harrison and Derek Holland on the disabled list, Scheppers became the first pitcher since Fernando Valenzuela for the Los Angeles Dodgers in 1981 to make his first career start on opening day. Scheppers, who had 76 relief appearances last season, struck out two and walked three.
Texas went ahead 7-6 on Alex Rios' three-run homer in the third, but Philly got even in the fourth on Chase Utley's RBI single, the first of his three hits.
Revere also had three hits, drove in three runs and scored twice. He hit .305 last season, but missed the entire second half with foot problems.
Lee got a nice ovation for Rangers fans before pitching in Texas for the first time since starting for the Rangers in Game 5 of the 2010 World Series. The lefty also made a season-opening start there for Cleveland in 2009, when the then-reigning AL Cy Young winner allowed seven runs over five innings in a 9-1 loss.
Rollins made his 14th straight opening-day start for the Phillies, matching Cal Ripken Jr.'s major league record with Baltimore for the most consecutive seasons starting at shortstop for the same franchise.
With his 200th career homer, the Phillies' starting shortstop since 2001 became the 19th player in major league history with at least 400 doubles, 100 triples and 200 homers.
Shin-Soo Choo and Prince Fielder, the big additions for the Rangers after they missed the playoffs last season for the first time in four years, were a combined 1-for-9. Fielder singled and scored on the Rios homer.
Notes: Josh Wilson, the journeyman starting at second base for Texas in place of injured Jurickson Profar, had a three-run double. ... It was the earliest interleague game in MLB history. ... The front-row seat by the Rangers dugout where Nolan Ryan used to sit was occupied by former Rangers and Phillies player Michael Young, who retired during the offseason. ... The national anthem was performed by the Fort Worth Symphony Orchestra, 20 years after they accompanied the late Van Cliburn, an award-winning classical pianist who lived in Fort Worth, for a stirring rendition before the first regular-season game ever played at the stadium. ... Hall of Fame third baseman Mike Schmidt holds the Phillies record for consecutive starts on opening day with 16 (1974-89).