For the second night in a row, they played big in a winning ninth-inning rally.
"It's really special for us," said Choo, who signed a seven-year free-agent deal with the Rangers this winter.
"That's why you play nine innings, and that's what we do every night is play nine innings," manager Ron Washington said. "In the end, we did what we had to do. We got focused and put some good at-bats together and made things happen."
Beltre, whose ninth-inning single Tuesday night drove home Choo with the winning run, started this three-run rally with a leadoff single. After Mitch Moreland's double, pinch hitter Jim Adduci had an RBI infield single and Leonys Martin singled home the tying run. Donnie Murphy walked on four pitches before Choo got to a full-count pitch before walking.
Adduci reached on a slow roller down the third-base line with one out before Martin grounded a single through the drawn-in infield.
"The whole inning was kind of just one of those innings. You get a cue ball down the third-base line. Then you get a double-play ball, which you think is the game-ending double play. It's not," said Papelbon, who gave up four hits and two walks while retiring only one batter. "My whole focus was get a ground ball, get a double play and get us out of the inning."
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.
"It's a nice way to start the season," Moreland said. "We really came together these last couple of games."
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 in August -- first on an interim basis 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.
After Philly got an unearned run in the first after center fielder Martin bobbled the ball for an error, Texas failed to score in the bottom of the inning after two hits 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.
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.