A couple of Magpies handling errors gave the hosts some attacking possession but Hawke's Bay used a significant first half tailwind to clear effectively.
From a scrum just inside their own half, Hawke's Bay found space on the blindside with Stacey Ili and Neria Foma'i combining to set Lolagi Visinia up for the first try on the quarter-hour mark.
Consecutive penalties to Canterbury saw openside flanker Solomone Funaki yellow carded for entering a maul from the side.
The hosts made their advantage pay immediately with a 26th-minute try to Ngane Punivai in space out wide.
The right wing thought he had a second five minutes later but the try was ruled out for his push on Foma'i off the ball.
Hawke's Bay's five-point buffer survived until Funaki's return and Marino Mikaele-Tu'u won a penalty for holding on, to give McClutchie another three points off the tee.
A scrum five metres out allowed the Magpies one more chance with the wind but Mikaele-Tu'u was held up over the line right on halftime.
Canterbury had superior territory and possession in the first half and with the wind they were able to put Hawke's Bay under even more pressure.
A scrum penalty allowed first five-eighths Fergus Burke to kick a penalty goal in the 47th minute and get Canterbury within one score.
The Magpies replied with their first attacking possession of the second term, building towards a try to Ollie Sapsford.
The right wing was denied another by Rameka Poihipi's cynical early tackle, earning him a yellow card in the 53rd minute.
Captain Brad Weber scored Hawke's Bay's third try next to the posts after a big attacking scrum.
They knocked the restart on though, allowing Canterbury to set up shop in the red zone.
Substitute Isaiah Punivai and Billy Harmon scored tries in quick succession to get Canterbury within three points.
A Burke penalty goal completed the comeback by the time Poihipi returned with 12 minutes remaining.
Another outstanding Lincoln McClutchie performance ended early.
Starting fullback Caleb Makene had come off in the game's opening moments after an head injury assessment (HIA), so Danny Toala saw out the game at first receiver with Ereatara Enari on the wing.
Weber took over the kicking duties and slotted a penalty goal to put Hawke's Bay in front with five minutes left.
Canterbury openside flanker Tom Christie's try gave Canterbury their first lead of the game with two minutes to play.
The Magpies went through more than 20 phases and Canterbury were penalised for not rolling away two minutes after the final siren.
Hawke's Bay were gaining ground into the 22 but Danny Toala opted for a grubber kick, allowing Canterbury to put the ball out and win the game.
The Magpies' next match is a Ranfurly Shield defence against Southland at McLean Park on Saturday afternoon.
Canterbury 32 (Ngane Punivai, Isaiah Punivai, Billy Harmon, Tom Christie tries; Fergus Burke 3/4 cons, 1/1 pen)
Hawke's Bay 28 (Lolagi Visinia, Ollie Sapsford, Brad Weber tries; Lincoln McClutchie 2/2 pen, 2/3 cons, Brad Weber 1/1 pen)
HT: 5-13
