The Reds looked in danger of suffering only their second home defeat of the season before Sacha Opinel equalised Lee Boylan's strike six minutes from time and Harkin kept his cool from the spot.
Defeat was harsh on Canvey who had dominated the first half and gone ahead after just eight minutes.
The Crawley defence failed to deal with a free-kick form the right wing by Chris Duffy and Boylan stole in to head into the roof of the net from the edge of the six yard box.
Boylan almost added another four minutes later with a curling effort which home keeper Phil Smith did well to push wide at full stretch.
Crawley were struggling going forward and they almost conceded again before half time.
Dominic Sterling volleyed just wide form close range after skipper Ian Simpemba had headed a cross into his path.
John Keeling then had an angled shot blocked at point blank range by Smith after he had beaten Simpemba with a clever step over.
Crawley were a different side after the break but had to wait until the 85th minute to get back on level terms.
Opinel, making only his third league appearance for Crawley, headed home his first goal for the club despite the best efforts of Chris Potter.
Substitute Harkin won it for the Reds a minute into injury time after Steve Ward had been sent off for a second bookable offence for a foul on Allan Tait.
Defeat was harsh on Canvey who had dominated the first half and gone ahead after just eight minutes.
The Crawley defence failed to deal with a free-kick form the right wing by Chris Duffy and Boylan stole in to head into the roof of the net from the edge of the six yard box.
Boylan almost added another four minutes later with a curling effort which home keeper Phil Smith did well to push wide at full stretch.
Crawley were struggling going forward and they almost conceded again before half time.
Dominic Sterling volleyed just wide form close range after skipper Ian Simpemba had headed a cross into his path.
John Keeling then had an angled shot blocked at point blank range by Smith after he had beaten Simpemba with a clever step over.
Crawley were a different side after the break but had to wait until the 85th minute to get back on level terms.
Opinel, making only his third league appearance for Crawley, headed home his first goal for the club despite the best efforts of Chris Potter.
Substitute Harkin won it for the Reds a minute into injury time after Steve Ward had been sent off for a second bookable offence for a foul on Allan Tait.