"I wanted to show them something," said Napoli, who raised his average to .323 and added a walk on the day to boost his on-base percentage to .432.
Kendry Morales also homered to propel the Angels to their 10th win in their last 14 games and secure their fifth straight series while Orlando Cabrera went 2-for-3 with a run and a walk to extend his streak of reaching base to 38 games.
The Angels head home with a 4-2 mark on the road trip and will open a 10-game homestand, beginning with a three-game set against the Mariners on Friday. Kansas City will follow with the Padres on their heels as baseball begins the next phase of Interleague Play.
"What I liked a lot about a game like today was [Vladimir Guerrero] goes 0-for-5 but we get a win," manager Mike Scioscia said. "That means we're getting production throughout the lineup."
But it was Napoli's blow to cap a two-out rally in the top of the fourth that provided the difference.
"I just kind of reacted and it happened," Napoli said. "It wasn't that bad of a pitch. I put a good swing on it."
The Angels reached double digits in hits for the fourth straight game and were treated to three highlight-reel defensive plays. Guerrero robbed Damon Hollins of extra bases at the right-field wall to end the fifth. Left fielder Juan Rivera made a sliding grab to rob Ty Wigginton in the sixth and center fielder Chone Figgins charged and slid to catch a sinking liner off the bat of Jorge Cantu in the seventh.
"Juan Rivera, Chone Figgins and Vlad made some key plays that helped us," Scioscia said. "We talked a lot about the importance of defense and that was key for us today."
Weaver turned in his third straight victory in as many starts to open his Major League career and all it might earn him is a trip back to Triple-A Salt Lake when Bartolo Colon returns, possibly as early as Sunday. But he's making the most of his time in the bigs and Wednesday he improved to 3-0.
The right-hander sailed through his first three innings, allowing one baserunner when he hit Cantu with a pitch in the second. Carl Crawford got the first hit off Weaver when he led off the fourth with a homer while Julio Lugo homered in the sixth. The right-hander allowed two runs on four hits with four strikeouts and no walks over six innings.
Napoli worked with Weaver a lot last season when both were at Double-A Arkansas and the pair have formed a strong rapport.
"It's good for him to come up here and show what he is really about," Napoli said. "It was fun to catch him."
Weaver did not allow a ground ball until Jonny Gomes yanked a double down the left-field line in the sixth and he didn't got his first groundout until Aubrey Huff bounced one to short two batters later. He got 13 outs on fly balls.
"It is usually not that many. I definitely go with a lot of fly balls," Weaver said. "I think the deception has something to do with it. The ball gets on hitters quicker and they don't get much on it."
Weaver's long limbs creates a motion that swings around his body before delivering the ball from three-quarters that makes it tough to pick up.
"He is a pitcher that moves the ball in and out and up and down," pitching coach Bud Black said. "He is the type of pitcher that creates the mis-hit."
In the fifth, Cabrera lifted a sac fly to center and Morales put another run on the board when he led off the sixth inning with a homer to right. Then in the seventh Cabrera hit a one-out double to center and scored on Garret Anderson's RBI single to left to build a 6-2 lead.
Rays starter Seth McClung (2-8) allowed five runs, four of which were earned, on six hits and three walks with one strikeout over 5 1/3 innings to take the loss.