The Sky Blues have fought from behind to earn a point at the Ricoh thanks to Marc McNulty's second half strik
The 25-year-old came close on a number of ocassion and nearly gave City victory late on but he could not connect with Jack Grimmer's hard-hit cross as the visitors clung on to a point.
Duckens Nazon struck the post from range in the first half but it was Crawley who led at the break through Jordan Roberts.
Mark Robins' side now sit sixth in SkyBet League Two.
Nazon was back in the starting eleven after serving his one match suspension. The Haitian Interntional looked lively coming inside from the left wing and fired the game's first shot wide of the far post from 25-yards.
Nazon's constant drifiting inside gave the 23-year-old plenty of sights at goal, but it would have Marc McNulty claiming the Sky Blues' second chance of the afternoon had it flew in off the post. Stuart Beavon did well to hold up play before finding Nazon again on th edge of the area before he unleashed a rocket that flicked up off McNulty's toe and rattled the frame of the goal.
Mark Robins' side dominated the first half, but the Sky Blues boss was forced to change his half-time team talk late on when the Reds snatched the lead moments before the whistle.
Panutche Camara broke free downt he right catching City unawares before he rolled a delicate ball across the six yard box for Jordan Roberts to slot home from close range and give Harry Kewell's side an unlikely lead.
The Sky Blues started the second half even stronger. Nazon again did well to create another chance for McNulty but the striker opted to cut back inside instead of shooting with his left and was crowded out.
The former Portsmouth man would make amends with twenty minutes left on the clock. Ryan Haynes charged down the left before picking out Nazon, who knocked the ball down for the for McNulty to blast past Glenn Morris and into the Crawley net.
City were more dominant than ever, and McNulty almost doubled his and the Sky Blues' tally moments after, but neither him nor Jordan Shipley could get on the end of Grimmer's low cross to giv City the win.
Coventry City 1-1 Crawley Town
Yellows: Randall (2'), Davies (29')
Reds:
Goals: Roberts (42'), McNulty (74')
Attendance: 6,381 (159 away)
Coventry City XI: Burge (GK), Grimmer, Davies (Stevenson 45'), Willis, McDonald, Haynes, Doyle (C), Shipley (Dev. Kelly-Evans 82'), McNulty, Nazon, Beavon (Ponticelli 69').
Subs: O'Brien (GK), Stokes, Maycock, Biamou.
Crawley Town XI: Morris (GK) (C), Young, Payne, Connolly, Boldewijn (McNerney 82'), Roberts, Yorwerth, Evina, Bulman (Djalo 82'), Randall, Camara (Meite 75').
Subs: Mersin (GK), Doherty, Lelan, Lewis.