Altidore's fourth and fifth goals of the season came in the 50th and 63rd minutes, respectively, and followed the ninth goal of the season by Juan Pablo Angel in the 24th minute.
Angel also assisted on one of Altidore's goals.
Less than four minutes into the match, Dave van den Bergh failed to convert on two solid chances for the Red Bulls, who have won two of their last three games to make their record 9-7-3.
It was the first time since a contest against Chivas USA July 26 that New York fielded a nearly healthy lineup.
Sunday's outcome left expansion Toronto with three losses and a tie in its last five games.