Cahill's quick tally 9 seconds into the game was the fastest goal in league history.
Ibrahim Sekagya and Bradley Wright-Phillips each added a second-half tally for the Red Bulls (16-9-8), who won back-to-back games in Houston for the first time in franchise history.
New York improved to a league-best 56 points -- one better than Sporting Kansas City -- as the two vie for the Supporters Shield, indicative of the year's best regular-season record.
Houston (13-11-9) ended the day one point out of an Eastern Conference playoff spot but could advance to the post-season.
The Dynamo need to post at least a draw against D.C. United next week along with a draw or loss by Philadelphia and a loss by New England.