ANAHEIM, Calif. — Alex Rodriguez limited the celebration of his latest playoff homer to a brisk trot and a few high-fives. CC Sabathia barely even pumped a fist while mowing down the Angels for eight innings.

Even while they shined at a pivotal point in the AL championship series, the slugger and the workhorse starter seemed determined to stick to business.

Although none of the Yankees’ 26 World Series championships included these two stars, their no-nonsense excellence in a 10-1 victory on Tuesday night put New York one win from routing the Los Angeles Angels and playing for another title.

‘‘We just need to close it out,’’ Sabathia said simply. ‘‘It’s that time.’’

Rodriguez homered in the third straight game of his outstanding postseason, Sabathia pitched five-hit ball on three days’ rest, and the Yankees took a 3-1 lead in the best-of-seven ALCS with superstars living up to their big contracts.

Johnny Damon added a late two-run homer for the Yankees, who could sew up their first trip to the World Series in six years with a win in Game 5 on Thursday night at Angel Stadium. New York’s A.J. Burnett faces Angels ace John Lackey.

Rodriguez had three hits and scored three runs, while Melky Cabrera drove in four for the Yankees, who built a commanding cushion in this once-wild series by draining the drama from it.