Bradley Wright-Phillips struck a hat-trick and Thierry Henry was also on the scoresheet for Mike Petke's side, last season's Supporters' Shield winners.
The win, the Red Bulls' second in eight league games, lifted them into third in the Eastern Conference, while Houston – winless in five – slipped to eighth.
The hosts needed just 12 minutes to open the scoring at the Red Bull Arena.
A fine passing move led to Henry being released down the right and the former Arsenal and Barcelona striker's cross found Wright-Phillips unmarked to poke in from close range.
It was a counter-attack that led to the lead being doubled in the 24th minute.
New York won possession and broke through Henry, who released Roy Miller down the left.
The Costa Rican's slide ensured he held onto the ball before picking out the run of Wright-Phillips, who beat his marker and side-footed into the bottom corner.
Henry was at it again for the Red Bulls' third goal just after the hour mark.
The 36-year-old played Wright-Phillips through and while the attacker was unable to complete his hat-trick, Henry reacted quickest to strike after Tally Hall had parried the shot.
Wright-Phillips' chance to complete his treble came from the penalty spot on 86 minutes, and he duly converted to top off the rout.
