Reds made a winning start to the Sky Bet League 2 campaign with a hard-fought win at the Jonny-Rocks Stadium.
Cheltenham has not been a happy hunting ground for Crawley in recent years but Ollie Palmer's header in the 63rd-minute continued our impressive opening-record with only one game lost in eight on the first day of the season.
Palmer rose highest to head in Filipe Morais's corner via the left-hand post - a dream start on his competitve debut for the striker.
Crawley were good value for their win, despite the hosts missing a second-half penalty.
Cheltenham's Scott Flinders was the busier keeper, brilliantly denying Josh Payne when he let fly from inside the box in the 22nd minute before making another good stop late on when substitute Panutche Camara got through. He also denied Dannie Bulman and Dominic Poleon, who loooked a real threat up front, in the first half.
It was a game of few clear-cut opportunities and for long periods was predictably cagey with neither side prepared to gamble too much on the opening day.
But Reds once again played some of the eye-catching football that Harry Kewell instilled last season and they kept possession well on a hot afternoon.
Cheltenham had their moments. Glenn Morris made a terrific save in the first half to deny Manny Duku but Reds had a let-off in the 72nd minute when Lumbombo Kalala was brought down in the box by Romain Vincelot but Kevin Dawson's penalty hit the bar.
Reds battened down the hatches in the closing stages while looking to counter-attack before celebrating with the 141 travelling fans at full-time. What a start to the season!
Reds: Morris, Young, Vincelot, Connolly, Doherty, Morais, Bulman (Randall 78), Payne, Francomb, Palmer (Camara 90), Poleon (Grego-Cox 66).
Pictured: Ollie Palmer celebrates his second-half winner.