"When this guy stays on the ball and gets pitches in the strike zone, he is an extremely dangerous man," Houston manager Bo Porter said of Carter. "Tonight was no exception. He sparked us."
The victory ended Tampa Bay's winning streak against the Astros at seven and moved Houston to 13-11 this season in one-run games.
Carter now has 17 home runs this year, and Wednesday's was the second multihomer game of his career, with the other coming April 9 against Seattle.
"You've got to give them credit the way they bounced back today, and their pitcher set up the whole thing," said Tampa Bay manager Joe Maddon.
Coming off a 20-0 aggregate in the Rays' favor through the first half of the series, it looked like more of the same early Wednesday.
Desmond Jennings singled off Norris and swiped second before moving to third on Matt Joyce's infield single. That gave the Rays runners on the corners before a single out had been recorded.
"I was in a jam four pitches into the game," Norris said. "You never expect that."
But Norris coaxed a run-scoring sacrifice fly and retired the next two batters to limit the damage. He cruised after that, allowing multiple baserunners in just one other inning.
"He did a great job minimizing the damage," Porter said. "He was able to do that by using all of his pitches and was able to get out of a jam that could've been a crooked number. It set him up for the next six innings."
The righty was far from perfect, issuing three walks and giving up six hits over seven innings. However, considering the damage Tampa Bay inflicted on Dallas Keuchel and Erik Bedard the past two games, Norris' start was a revelation.
"Bud was absolutely outstanding," Porter said. "I thought he threw probably the best game of his season. His slider just had unbelievable depth. he had a great two-seam fastball, and he pitched to both sides of the plate. He even had his changeup, a third pitch, working.
"He's our No. 1 guy, and he pitched like an ace tonight."
Norris struck out five and threw 105 pitches, 64 for strikes.
With the outing, he lowered his ERA to 2.28 in 11 home starts this season. Despite that low average, Norris was only 3-3 at home before Wednesday's win, thanks to some low run support.
"He's been stuck on five [wins total] for his last three or four starts," Carter said. "We made it a mission to get him to six, since he's been pitching well for us."
The Astros needed Norris, because the struggles on offense continued outside of Carter, though it took only a couple of his big swings to break a 22 2/3 inning scoreless streak.
In the second, Carter swung and missed at the first two pitches from Tampa starter Roberto Hernandez, seeming poised to go down quickly on strikes. But his newfound patience kicked in, as he worked the count full and dug out a fastball well over the left-field wall.
"Chris fouled off some tough pitches, laid off some tough ones and was patient enough to get the ones that he can drive," Porter said. "He didn't miss them tonight. Those balls were squared up pretty good."
Dormant for four innings after Carter's solo shot, the Houston offense woke up in time to set the stage for the slugger again, this time in go-ahead fashion.
Brett Wallace doubled to open the seventh, gracefully sliding in to beat the tag before he moved to third on Jason Castro's single.
"That slide was the biggest part [of the inning]," Carter said. "If he slides in straight, he's probably out, but he went in crooked and got things started."
Hernandez's night was done, as reliever Jake McGee entered with no outs.
Carter again worked the count full, and on the eighth pitch he delivered the dagger with a colossal go-ahead, three-run homer that banged off the Astros' community leaders logos near the train tracks.
"I was just trying to get the ball in the air, with a runner on third in a tie-game situation," Carter said. "He kept throwing fastballs away, and I kept fouling them off. I ended up getting a hold of one. It was a no-doubter."
After allowing a combined 11 runs the previous two nights, the Houston bullpen shut the door Wednesday.
Reliever Jose Cisnero set the Rays down in order in the eighth, and Jose Veras earned his 17th save in 20 attempts with a scoreless ninth.
Chris Abshire is an associate reporter for MLB.com.