Trumbo, who entered with one hit in 20 at-bats over his previous seven games, had two hits, including a two-run homer off Price. The Angels have won nine of 13 road games this year.
"This guy is one of the aces of our league and I thought we did a good job," Angels manager Mike Scioscia said of Price. "Good at-bats. Got his pitch count up. When he missed with some pitches, we squared him up. We were able to pressure him for his whole outing and that's what we have to do against good pitchers."
Price (3-3), coming off three consecutive wins, gave up five runs and a career-high 12 hits in 4 1/3 innings. The left-hander had given up six runs and 17 hits over 23 2/3 innings in his previous three starts.
"Obviously, they swing the bats really well against us," Rays outfielder Matt Joyce said. "We've got our best pitcher going on the mound and they still put up a lot of hits and a lot of runs. It seems like they play really well against us."
The Angels swept a two-game series at Tampa Bay earlier this month.
Santana (1-3) stopped a personal seven start winless streak, dating back to last season, by allowing four runs -- one earned -- and four hits over six innings.
Joyce hit a three-run homer for the Rays, who had won five in a row.
Erick Aybar had an RBI infield single and Trumbo added a two-run homer that tied it at 4 in the fourth.
Vernon Wells hit a fifth-inning sacrifice fly to put Los Angeles ahead 5-4. The Angels took a 7-4 lead in the seventh when Alberto Callaspo drew a bases-loaded walk and Aybar hit a run-scoring grounder.
Trumbo also had a ninth-inning RBI grounder. The four RBIs tied his career high, set on April 19 against the Texas Rangers.
The Rays went up 4-1 when Joyce hit a three-run shot with two outs the third. Reid Brignac reached to start the inning when Aybar was charged with an error at shortstop after misplaying a high pop fly.
"He pitched a strong game, especially bouncing back after we muffed that pop up," Scioscia said of Santana. "He came back and put up some zeros and that was important."
After Scott Downs threw a scoreless seventh, Fernando Rodney allowed an eighth-inning solo homer to B.J. Upton that cut the Los Angeles advantage to 7-5. Jordan Walden pitched the ninth for his fourth save.
Trumbo put the Angels up 1-0 with an RBI single during the second. Tampa Bay got the run back later in the inning when Zobrist walked and scored on Casey Kotchman's double.
Joyce was ejected in the sixth by plate umpire Tom Hallion for arguing a called third strike.
Tampa Bay DH Johnny Damon was hitless in four at-bats and had his 16-game hitting streak end. ... Los Angeles second baseman Howie Kendrick went 3-for-4 and has 47 hits in 104 at-bats overall against Tampa Bay. ... Rays infielder Sean Rodriguez (dislocated left pinkie finger) will have his status updated this weekend. ... Angels infielder Maicer Izturis (sore left hamstring) could play on Saturday. ... Tampa Bay left-hander J.P. Howell (left shoulder surgery) is set to join Triple-A Durham after pitching Sunday for Class A Charlotte. ... Los Angeles left-hander Scott Kazmir (sore lower back) is scheduled to pitch in extended spring training early next week. ... Tampa Bay manager Joe Maddon became a grandfather for a third time after the birth of a grandson Friday in Arizona.