The Rangers scored three times in the ninth off Papelbon (0-1), who gave up four hits while retiring only one batter.
Adrian Beltre, whose ninth-inning single Tuesday night drove home Choo with the winning run, started this rally with a leadoff single. After Mitch Moreland's double, pinch-hitter Jim Adduci had an RBI infield single and Leonys Martin singled through a drawn-in infield to drive in the tying run. Donnie Murphy walked on four pitches before Choo got to full-count pitch before walking.
Seth Rosin (1-0) worked two scoreless innings for his first major league victory.
Moreland had a triple in the seventh and scored on Martin's two-out single.
Ryan Howard hit a two-run homer and Kyle Kendrick allowed only one run over seven innings for the Phillies, who still haven't won a road series since Ryne Sandberg took over as their manager last August - first on an interim bases before getting the full-time gig.
The Phillies lost 24 of 32 games over their final 10 road series last season. They split four games against the New York Mets last August in Sandberg's first series on the road - but had dropped the previous five series away from home, and then lost the last four. They won this year's season opener 14-10 before consecutive ninth-inning losses.
Texas left-hander Robbie Ross struck out seven over five innings in his first major league start after 123 relief appearances the past two seasons. He allowed three runs and seven hits with two walks.
Howard's homer made it 3-0 in the third. It was his first homer since July 5, when he went deep in his final game last season before going onto the disabled list because of left knee inflammation.
Kendrick struck out four and allowed one run, but is still winless his last eight starts. The right-hander went 0-5 over his final seven starts last season, when the Phillies scored a combined two run behind him in those losses.
Philly got an unearned run in the first when Carlos Ruiz had a one-out double and scored only after center fielder Martin bobbled the ball for an error on Chase Utley's single before Howard and Marlon Byrd both took called third strikes.
Texas failed to score in the bottom of the first despite consecutive singles by Choo and Elvis Andrus and two errors by the Phillies. Choo got caught in a rundown and tagged out between third base and home after Kendrick initially dropped a grounder.
NOTES: The Phillies were a player short after SS Jimmy Rollins returned home to be with his wife for the birth of their second child. ... Texas said ace RHP Yu Darvish will make his season debut Sunday at Tampa Bay. He was put on the disabled list because of neck stiffness. ... Rangers INF Adam Rosales cleared waivers and accepted his assignment to Triple-A Round Rock. ... Both teams are off Thursday before road games Friday. The Phillies play the Chicago Cubs for the opener marking the 100th anniversary of Wrigley Field, and the Rangers are at Tampa Bay. ... Super Bowl-winning QB Russell Wilson threw out the first pitch. The Rangers selected Wilson from the Colorado Rockies in the Triple-A portion of baseball's December draft at the winter meetings. ... Ross threw 96 pitches. His previous career high had been 45.