Gillingham also finished with 10 men after Luke Rooney received his second booking in stoppage time.
Crawley were a man down after 18 minutes when centre half Claude Davis was shown a straight red card for bringing down Kuffour on the edge of the area and Danny Jackman put the resulting free-kick just wide.
But he npower League Two leaders broke the deadlock 11 minutes before the break when a clumsy tackle by Matt Lawrence flattened Kyle McFadzean in the area and striker Matt Tubbs stepped up to blast home the resulting penalty.
Kuffour struck twice inside two minutes at the start of the second half to turn the match in Gillingham’s favour. First he ghosted in at the far post to fire in a cross by Chris Whelpdale in the 50th minute before beating three defenders to hit the winner with a superbly taken individual goal.
There was late drama when Lawrence hacked a Tubbs effort off the line to deny Crawley an equaliser.