Albert Pujols reached the 100-RBI mark for the 11th time in 12 big-league seasons with a two-run double as the Angels remained 2 1/2 games behind Oakland for the second wild card. Kendrys Morales hit a two-run homer that helped the Angels complete a three-game sweep.
"Obviously there's a little bit of scoreboard watching going on now as we dwindle now here," Weaver said. "But we've got to do what we've got to do and not worry about what other teams are doing. It's obviously a great sweep, and hopefully we can keep it rolling against Seattle."
The White Sox lost their fifth in a row and lead Detroit by one game in the AL Central.
Weaver (19-4) threw 113 pitches in 6 1/3 innings, allowing a run and five hits with four strikeouts and dropping his ERA to 2.74.
The win didn't come easily for Weaver, who battled through 94-degree heat during a 33-pitch first inning. He escaped a bases-loaded jam, striking out Alex Rios at the end of an 11-pitch at-bat and retiring A.J. Pierzynski on a grounder.
"It felt like it was a million degrees out there," Weaver said. "Having to throw upwards of 30 pitches in the first is obviously not what you want to do, but they made me work. That's what their game plan was, and they did a good job of it."
White Sox manager Robin Ventura bemoaned his team's failure again to come through in the clutch. They were 1-for-17 with runners in scoring position in the series. "We had Weaver in trouble early and were in a really good position, but he showed again why he's a good pitcher and we just couldn't cash in," Ventura said.
In other games: *
At Seattle, Ryan Dempster (12-7) allowed two runs and six hits over six-plus innings and Mike Napoli and Geovany Soto homered to lead Texas to a 3-2 victory over the Mariners. The Rangers were again without Josh Hamilton, who has missed the last five games with a sinus issue that's affecting his vision.
* At New York, Cliff Pennington hit a go-ahead single in the sixth inning after a key error by backup shortstop Eduardo Nunez and the Oakland Athletics bounced back to avoid a sweep, with a 5-4 win that halted the Yankees' seven-game winning streak.
* At Boston, Cody Ross doubled in the go-ahead run in the eighth inning, Andrew Bailey escaped a bases-loaded jam in the ninth and the Red Sox ended Baltimore's six-game winning streak, beating the Orioles, 2-1.
* At St. Petersburg, Fla., B.J. Upton hit his eighth home run in 14 games and Jeremy Hellickson (9-10) won for the first time in more than a month to help the Tampa Bay Rays beat the Toronto Blue Jays, 3-0.
* At Detroit, Jamey Carroll hit an RBI single in the 10th inning and the Minnesota Twins beat the Tigers, 2-1, winning both games of a doubleheader to prevent Detroit from at least tying the White Sox atop the AL Central.
Joe Mauer drove in four runs to help the Twins rally against Max Scherzer and pull away for a 10-4 win in the first game.
* At Kansas City, Carlos Santana hit two homers and drove in five runs as the Cleveland Indians routed the Royals, 15-4.