The Seasiders dominated the first half producing sufficient chances to have been comfortably ahead by the interval thanks to David Pounder, who was in fine form, and Scott Kerr, giving one of his best performances of the season.
At the other end, Simon Wormull threw away a good chance to put Crawley ahead with a free-kick from the edge of the penalty box which he ballooned high over the bar.
A well-placed Kevin Nicholson corner found Sarborough's Mark Hotte on the spot, but his header went just wide of the near post.
Nicholson went on to test Crawley keeper Phil Smith, who produced some fine saves.
As half-time approached, Crawley strove to get more of the play with Robert Kember landing a 35-yard volley on to the roof of the net and Paul Armstrong going close with a hard drive from the left which keeper Leigh Walker did well to save.
Armstrong and Neil Jenkins each put the Scarborough defence under pressure before Crawley took the lead in the 37th minute when Allan Tait seized his chance after Paul Foot failed to clear in the goalmouth.
Scarborough had chances to get back into the game and succeeded two minutes before the break when Tony Hackworth stabbed the ball in the bottom corner of the net from a great cross by Colin Cryan.
Tait and Charlie MacDonald worked hard to put Crawley back in the lead after the re-start and the visitors' pressure paid off in the 58th minute when Armstrong blasted home a brilliant free-kick from just outside the penalty area.
However, six minutes later Scarborough came back into the game when Hotte headed down a Nicholson free-kick which Pounder put home, and in the end a draw was a fair result.
Nick Henry, the Scarborough manager, said: "We did well to come back twice and that was great credit to the lads for the hard work because in the end we almost won the game."
Crawley manager Francis Vines said : "I would have settled for a draw before the game because we knew it was going to be difficult. I was sorry we gave away the second goal, but overall I was very satisfied with my side's performance."