Town boss Ian Sampson was unhappy that his side had a late 'goal' chalked off and opposite number Dario Gradi admitted: "We've had a bit of luck but I'm not going to feel guilty as we deserve some.
"I couldn't see it properly from my angle but if you ask me then it was definitely not over the line!"
Crewe fought back from 2-1 down to take the points and Gradi added: "It was a terrific victory but I couldn't see it coming at one point."
The Railwaymen now lie 14th in League Two, two places below Northampton.