The winger had only been on the pitch a matter of seconds when he stooped low to head home Matt Tootle's cross at the back post in the 80th minute.
There had been few previous flashpoints in a low-key match, with Crawley's Jamie Proctor having the best chance of the first half when he crashed a shot against the crossbar.
The visitors were handed a one-man advantage when Crewe's Vadaine Oliver was sent off in the 55th minute.
The forward received two yellow cards, his first for a leading elbow and the second for what looked like a clear dive.
But Crawley failed to make the most of it, with Nicky Adams testing goalkeeper Neil Etheridge and Mat Sadler having a shot cleared off the line.
And after Aneke's whirlwind introduction, Andy Drury somehow headed over at the other end as Town extended their winless run to eight.