After missing two attempts from long range in the final 90 seconds of regulation time, the Bulldogs five-eighth made no mistake with his third attempt directly in front from 38 metres out.
The shot came just seconds after Sharks halfback Nicho Hynes had the chance to snatch Friday night's game for the slow-starting visitors.
In his first game since being axed as NSW halfback, Hynes shanked his attempt from straight in front at point blank range, instead handing Canterbury a seven-tackle set.
The Bulldogs marched to the other end of Accor Stadium, where Burton sealed a victory that keeps the NRL's big improvers inside the top eight for another week.
Viliame Kikau began proceedings with a bang for the Bulldogs, scoring in just the second minute. (Mark Evans/AAP PHOTOS)
Ladder leaders through 12 rounds, the Sharks have now dropped four of their past five games and will rue falling victim to old habits against the Bulldogs.
Coming off the bye, with almost their entire roster fit and without any State of Origin representatives backing up, there was little excuse for another slow start.
But Cronulla fell to 12-0 down after only 14 minutes, unable to defend early errors.
Usually-reliable Cam McInnes spilt the ball on only the third tackle of the night and the Bulldogs turned the ensuing field position into a try through Viliame Kikau, who beat Toby Rudolf and Braydon Trindall to his own kick.
Canterbury had their second try on the back of an offside penalty from Hynes, with Reed Mahoney scooting out of dummy half to extend the advantage a little too easily.
Reed Mahoney scored the second try of the game to help Canterbury to a 12-0 lead. (Mark Evans/AAP PHOTOS)
The Sharks had numerous close calls, with Hynes's inside ball to a flying Royce Hunt called forward just as the in-form prop looked destined to level the scores 12-12 with his try.
They eventually took the lead when Ronaldo Mulitalo somehow put boot to ball in a tackle from Jeral Skelton, with Trindall rushing down the short side to score in the corner with 19 minutes to play.
In the final five minutes, referee Gerard Sutton penalised Cronulla prop Toby Rudolf for obstructing Bailey Hayward's kick chase close to the line and Matt Burton's ensuing goal tied the game at 14-14.
Burton did the rest from there, sealing the win in the fourth minute of extra time.
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