By winning, the Rays (65-54) remained six games behind the AL East-leading Yankees while moving a game ahead of the Orioles into the top spot for the AL Wild Card.
Friday night's victory also ensured a winning record on the current 10-game road trip on which the team currently boasts a 6-2 mark.
Price did his job Thursday night by putting forth a dominant performance in a 7-0 Rays win. Rays hitters got after Weaver from the outset of Friday night's game.
Scioscia mercifully rescued Weaver in the fourth after watching his ace face seven hitters and not record an out. Weaver, who entered the game with a 15-2 record, gave up a career-high nine earned runs and watched his ERA swell from 2.22 to 2.74.
B.J. Upton homered off Weaver with one out in the first to give the Rays center fielder his fifth home run in eight games, beginning his four-hit, three-RBI evening. Ben Zobrist added his 14th homer of the season leading off the second to stake the Rays to a 2-0 lead.
"B.J.'s playing at this higher level," Maddon said. "I think the last time I saw something similar to this it was in the playoffs in 2008. It's fun to watch because I can really see that his focus is great. His confidence is soaring. You're starting to see the abilities matching the expectations. He's in a good place right now. ... B.J.'s home run really was a big moment for us. But then [Weaver] settled in and I thought it was going to be different."
For the second night in a row, Rays hitters hung a crooked number on the scoreboard in the fourth. Thursday night, they scored four. Friday night, seven Rays crossed the plate in the fourth.
Sean Rodriguez and Ryan Roberts started the onslaught with RBI singles. Jose Molina followed with a two-run single before Desmond Jennings doubled home another to chase Weaver.
LaTroy Hawkins took over and Upton greeted him with a two-run single to cap the Rays' fourth-inning scoring and close the book on Weaver.
"We got to him there in the fourth inning," Rays starter James Shields said. "He's a good pitcher. He's been pitching really, really well all season. I know as well as anybody, sometimes you're going to have bad days. But our team did a great job of getting to him early. He's a strike thrower and we got to him."
In the two games since Felix Hernandez pitched a perfect game against the Rays, the offense has produced 19 runs, 25 hits and six home runs.
"I think Felix Hernandez throwing a perfect game against us just kind of made us a little mad deep down inside," Shields said. "But we did a great job in these first two. Hope we can close it out."
Shields got all the breaks he needed in the first inning after Mike Trout tripled leading off. Shields then battled Torii Hunter for seven pitches before Hunter ripped a low line drive to third base. Rodriguez made a diving backhanded stab of the ball, then reached out while still on his belly to touch the bag and double off Trout.
"Roddy, that play in the first pretty much set the tone," Shields said. "Got the guys going. Got the guys lifted in the dugout."
Erick Aybar homered off Shields to lead off the third, snapping the Angels' scoreless streak against Rays pitching at 34 innings. The only other blemish on Shields' outing came in the fourth when Howie Kendrick hit a two-run homer.
Despite the two homers Shields surrendered, he still managed to give the Rays his 14th quality start of the season en route to notching his 11th win.
"Yesterday, the way Dave threw was amazing," Shields said. "Kind of got me pumped up personally, got the guys going.
J.P. Howell pitched a scoreless ninth for the Rays to set a club record for consecutive scoreless innings with 23 2/3 to surpass Shields' record of 23.