In the 4th inning, Teixeira unloaded a right-handed, two-run blast off starter John Danks for his 30th of the season and belted his 31st, batting left-handed in the top of the 7th, he victimized reliever Jason Frasor for number 31.
His three RBI gave Teixeira 82 on the season. He trails Boston's Adrian Gonzalez (90) for the AL RBI lead.
The Yankees scored another run in the 7th to make the score 6-0, just before relentless rain came to Chicago and the game was made official. Phil Hughes worked all six innings for the Yankees, allowing just three hits, fanning four without issuing any bases on balls.
The win kept the Yankees within one game of top-dog Boston in the AL East. The two teams meet in a weekend series beginning Friday at Fenway.
Pittsburgh's Cinderella story looks like it may not have a fairy tale ending as the Priates have slumped of late, losing 10 of their last 13 games and five straight, including their second straight loss to the Cubs, 11-6, on Tuesday.
While the Cubs have been out of the division race since June, they managed to bang six homers off the Pittsburgh pitching staff, including two solo shots - numbers 18 and 19 - by Alfonso Soriano and a two-run blast from Aramis Ramirez, his 20th.
Ramirez also drove in two runs with a single in the first inning to give him 67 RBI on the year.
TIGHT RACES: As the season quietly turned to August, pennant races have heated up in all but one division, the NL East, where the Phillies hold an imposing 8-game lead over Atlanta, the largest bulge, by far, in any divisional race.
In the NL Central, the Brewers hold a 2 1/2 game lead over the Cardinals, with Pittsburgh still lurking, 5 1/2 out, and the Reds 6 1/2 down. The NL West is now a shoot-out between Arizona and San Francisco. Each team holds a share of first place with identical 61-49 records. Arizona knocked off the Giants for the second straight day, beating them 6-1, and will be looking to sweep the series on Wednesday.
In the American League, all three races are tight. Boston leads the Yankees by one game in the East, while the Tigers cling to a three-game lead over the Indians in the Central, with the White Sox 5 1/2 back and Minnesota running out of time, eight games down.
The Al West has turned into another showdown between the Angels and Rangers, with Texas holding a one-game edge in the division. The two teams meet up in LA for a four-game series, August 15-18.