In a game dominated by the wet conditions and whistle of referee Tipene Cottrell, Tasman had been the better side in both areas.
But they also struggled to make that ascendancy count, with Mitchell Hunt's three penalties all they had to show for their efforts as they took a 9-7 lead to halftime.
Until the final quarter, Canterbury had been equally ineffective, with Burke providing one bright moment after cutting through the visitors' defence to score the game's opening try.
The hosts really should have added to that early advantage when Tasman saw their numbers twice reduced, as Lester Fainga'anuku and Sam Matenga both saw yellow.
The Mako were forced to play with 13 men for five minutes but spent the majority of that time with the ball in their hands, eventually welcoming back the sin-binned pair as Mitchell Hunt added three points at a time from the tee.
It was the hosts' turn for ill-discipline to cost them in the second spell, with Tasman for once opting against a shot and reaping the benefits of that decision through Quentin MacDonald's try.
But with the game threatening to slip away, Romano stepped up to hand his side a way back into the contest, cannily breaking away from a lineout drive to help cut the deficit to six.
Suddenly it was Tasman who continually found themselves earning the ire of Cottrell, with one penalty pulling Canterbury within three and several more seeing the home side set up camp on the opposition line.
All that pressure finally paid and McLeod made the pivotal impact, finding enough space in midfield to earn a vital victory.
Canterbury 24 (F Burke, L Romano, D McLeod tries; F Burke 3 cons, pen)
Tasman 20 (Q. MacDonald try; M Hunt 5 pens)
Halftime: 7-9
