In the victory, Clemens got the usual offensive barrage behind him, and the Yankees continued the best start in team history.
Clemens (4-0) improved to 28-8 lifetime against the Angels, his most wins against any team, after allowing two runs runs and six hits in eight innings, with no walks and six strikeouts.
"We're still three away," he said about getting career win No. 300. "I think as we get close, 299, the excitement will be there. I'll be focusing on that start. Being my last year, there's a lot of people I need to be there to watch it and give thanks to."
"I don't care how old you are, he was very effective," said Anaheim Manager Mike Scioscia.
The Yankees (18-3) posted their seventh straight win, and extended a remarkable streak as their starting pitchers improved to 16-0. New York is 6-0 on a 10-game road trip.
"I think it's amazing doing this with the guys they've lost out of the bullpen," said Scioscia, referring to Mariano Rivera and Steve Karsay.
The Yankees have scored 39 runs in Clemens' five starts, a stretch that includes a 2-1 loss to Tampa Bay in which he did not factor in the decision.
"I like to hit leadoff home runs to put my teammates on top," said Soriano, who already has done it three times this season.
He went for 4-for-5, extending his hitting streak to 11 games, and raising his average to .388. Soriano leads the major leagues in hits (38) and total bases (68).
"It's tough to put into words the team effort," said Yankees Manager Joe Torre. "Soriano is using both fields. You can't do it all year, but then every game ends and you think, 'Why not?'"
Facing the team that eliminated them in the American League Division Series in 2002, the Yankees have outscored the Angels, 17-5, in the first two games of the three-game series.
Mickey Callaway (1-2) took the loss, allowing six runs and 10 hits in 4 2/3 innings.