Jeremy Hellickson walked Kole Calhoun to lead off the game, then served up a two-run home run to Mike Trout in a three-run inning from which the Rays never quite recovered.
The Rays came back from a three-run deficit to load the bases with no outs in the ninth inning, only to have Angels closer Huston Street save it with strikeouts of Desmond Jennings and Ben Zobrist and a popup by Matt Joyce.
"We had every chance to win that game late," Rays manager Joe Maddon said. "Seven-eight-nine (hitters) load up the bases and here comes one-two-three and we can't get anything done. That's really disappointing.
"There are no moral victories; we've got to start winning games, and that's a game we should not have permitted to get away."
Trout's 25th homer and Josh Hamilton's seventh helped the Angels take the early 4-1 lead off Hellickson (0-1) before Hamilton left the game with a bruised left middle finger.
"I thought I settled down well after that," Hellickson said, "but to give up three in the top of the first, especially the way I did it -- walk, home run, double, then a single two batters later -- you just have to do better in the first inning."
Street got his fifth save since being acquired from San Diego on July 18. Zobrist had a potential game-winning hit go foul down the right field line.
This was the Rays' first game since trading Price to Detroit as part of a three-team deal Thursday.
Albert Pujols tied Chipper Jones for 26th place on the career list with his 549th double in the first and scored on Erick Aybar's single. Matt Shoemaker (9-3) allowed three runs and eight hits over five innings.
Tampa Bay got within 4-3 in the fifth on Evan Longoria's infield single. A second run scored on a throwing error by third baseman David Freese. Longoria was thrown out attempting to advance to second after colliding with first base umpire Larry Vanover.
Hellickson gave up four runs and six hits in 4 2-3 innings. The right-hander, coming back from right elbow surgery in January, has gone less than five innings in all three of his starts this season.
Angels: Tyler Skaggs was placed on the 15-day disabled list with a left forearm strain. Manager Mike Scioscia says the left-hander might miss "a little bit of time."
Rays: Right fielder Wil Myers, out since May 31 with a broken right wrist, took batting practice in an indoor cage for the first time. ... Catcher Ryan Hanigan (left oblique strain) will DH Saturday and catch Sunday in rehab games.
Angels: Left-hander C.J. Wilson (8-6) is scheduled to return from the disabled list to start Saturday night. He went on the DL July 10 with a sprained right ankle
Rays: Right-hander Chris Archer (8-6) is looking Saturday night to extend a stretch of going six or more innings in 10 of 12 starts.
The Angels arrived at their hotel just after 4 a.m. following a 1-0, 13-inning win Thursday night at Baltimore that took 4:33. Friday's game took 3:39
GUMBY MISSES OUT
The Rays are giving away Maddon "Mr. Potato Heads" on Saturday. Maddon is hopeful that there will be another promotion featuring his favorite character "Gumby" in the future.