Nowhere near the power hitter that Teixeira is, Abreu took a big first step to making up for the loss of the free agent.
"This is really my first game where I felt like I really helped them with the bat. I hope more of those are coming," said Abreu, who is hitting .309 with 19 RBIs, but just one homer.
Weaver (4-2) improved to 4-0 against Chicago while striking out eight in eight innings. He gave up four hits and one run. Weaver has now given up just one run in four of his last five starts.
"I was trying to make some good pitches early, trying to get some early outs, and I was able to do that for the most part," Weaver said. "Those guys can hurt you at any time, so you've just got to keep making your pitches, and mix it up a little bit."
Fuentes pitched the ninth to pick up his 13th save of the season.
Teixeira left after signing a $180 million, eight-year contract with the Yankees and the Angels signed Abreu on as a free agent on Feb. 12.
"Obviously, anytime you can get a guy like that, it definitely brings a smile to your face," said Weaver about Abreu. "He's done really well for us. His approach is just the same as Teixeira, along with his overall outlook on the game. His approach at the plate helps everybody and for the guys hitting behind him to be able see a lot of pitches when he's up is very helpful to them."
Floyd gave up three runs and seven hits in eight innings. He struck out eight and walked two, but was on the losing side for the fourth time in five games.
"I made a couple of bad pitches," Floyd said. "I told myself where to throw it and I didn't execute it. If I could rewind it again, I would. I made a couple of bad pitches and it hurt me."
White Sox manager Ozzie Guillen was satisfied with the outing.
"Gavin is throwing the ball really well the last couple of outings. He's regrouped himself and he's going in the right direction," Guillen said. "Before it was a clear struggle. But right now I think he has the confidence back and he's going to pitch great this summer."
Taking two out of three against the Angels, second in the AL West to Texas, wasn't so bad, either.
"Anytime you come here it's a gamble," said Guillen. "It's just not easy to go out and win two out of three."
A grand jury indicted the suspected drunken driver who prosecutors say killed Angels pitcher Nick Adenhart and two of his friends on April 9. Andrew Gallo is facing three counts of murder and three other felonies. ... Mathis' single in the sixth inning snapped a 0-15 hitting streak for the catcher.