Walsall manager Dean Smith praised his team's resilience after they fought back from two down to rescue a point with two goals in the last four minutes.
The Saddlers extend their unbeaten run to nine games with a 2-2 draw just as Crawley thought they had pulled off a shock win at the Banks's Stadium.
Smith said: "It says a lot for my team that they scored twice so late in the game and then went looking for the winner."
Crawley were seeing out time when the Saddlers pulled a goal back with a deflected shot from Jamie Paterson, who had earlier hit a post, in the 89th minute.
Then Will Grigg notched his 19th of the season from Andy Taylor's low cross in the third minute of stoppage time.
Crawley built a two-goal lead through Jamie Proctor and Paul Hayes but have now drawn their last four matches.
Manager Ritchie Barker said: "I'm very disappointed. Not with the performance, but that we didn't see it through.
"If I am honest Walsall hit a post but apart from that I didn't see them carving us open. I didn't see where one chance was coming from, let alone two.
"We have got to see games through. We are a young side and have got to learn very quickly.
"It's getting tougher for us to make the play-offs. We have lost only one in eight, but we've had too many draws when we needed win, and we have hit the woodwork five or six times in the last four games."