Weaver (7-4) won for the sixth time in eight starts, allowing two runs, five hits and four walks in six innings. His teammates staked him to a 7-1 lead through four.
''Coming back home, we wanted to set the tone and came in with a little fire under our butts,'' Weaver said. ''My curveball was pretty sharp and I was able to locate it when I needed to. As it turned out, it was a good pitch against that lineup. Those guys across the way have been swinging the bats well, and they've got a tremendous talent in (Jose) Abreu. So it was nice to quiet him down a little bit.''
The All-Star right-hander, pitching at home for the first time since his two-hit, 2-1 victory against Houston on May 21, struck out nine and improved to 8-2 with a 1.70 ERA in 11 starts against the White Sox.
Angels sidearming righty Joe Smith hit Alejandro De Aza and Adrian Nieto with consecutive pitches in the eighth, and nearly plunked Adam Eaton with his next offering before retiring him on a soft line drive to first with the bases loaded.
Pujols capped the Angels' scoring in the bottom half with his 15th homer and the 507th of his career. Adam Dunn capped his three-hit night with a two-run homer off Ernesto Frieri, his 10th this season and the 450th of his career.
''Me and Adam have been really good friends over the last 15 years and we actually played minor league ball together,'' Pujols said. ''He congratulated me today on hitting my 500th home run, saying he forgot about it, and I told him: 'Hey, it's OK. You might be the next one to do it.' I'm pretty sure he has a shot at it if he stays healthy.''
Andre Rienzo (4-3) lost his third straight start, throwing 72 pitches over 3 2-3 innings and giving up seven runs on nine hits. Over the previous 15 games, White Sox starters had a combined ERA of 2.03.
Chicago, starting its third straight series in Southern California, slipped 3 1/2 games behind AL Central-leading Detroit. After this series, the White Sox return home for a four-game showdown with the Tigers.
Calhoun got the Angels off and running with the second leadoff homer of his career, driving Rienzo's third pitch to right-center.
''He's bringing a lot of energy in that leadoff spot. And him getting that huge home run right away for us after a tough road trip was a big boost for us,'' Pujols said. ''He's a great player, and obviously we missed him during the time he was on the DL.''
Mike Trout followed the home run with a single, stole second and scored on a double by Josh Hamilton that ended his drought of 27 at-bats without an RBI against White Sox pitching.
De Aza got Chicago on the board in the third, leading off the inning with his fifth home run. The White Sox loaded the bases, but Weaver minimized the damage by slipping a called third strike past Dunn.
''I've faced him a lot of times - and I'm not going to give away any secrets - but I was able to locate a good two-seam fastball in there late and I caught him off guard,'' Weaver said. ''He's one of those guys who's going to punish you if you make a mistake.''
The Angels increased the margin to 7-1 with five more runs in the third. C.J. Cron hit a two-run double inside first base, Hank Conger snapped an 0-for-18 drought with an RBI single and Calhoun added a two-run double inside first base.
''That inning they just put it together and we couldn't stop them,'' Chicago manager Robin Ventura said. ''He got in trouble and just couldn't find a way out of it. We didn't get much off Weaver. We had some guys in scoring position and left a lot of guys on base.''
Abreu, the White Sox rookie sensation, ended up with a gift double in the second when his high fly fell in short right-center between Trout, Calhoun and second baseman Grant Green. But Weaver struck out Dunn and Alexei Ramirez before retiring Dayan Viciedo on a fly ball.
''Stuff like that is going to happen during the course of a game, and it's frustrating when it does,'' Weaver said. ''But it's our job as pitchers to pick those guys up when we need to. And from an offensive and defensive standpoint, those guys have to pick us up when we need it.''
Dunn drove in Chicago's second run with a fifth-inning single.
NOTES: Weaver fanned Abreu in the fifth for his 1,300th strikeout. ... The Angels are 32-20 when Calhoun plays, and 0-7 when he doesn't. ... Weaver has allowed a home run in five consecutive starts, one shy of his career-worst stretch in 2012.