Velupillay's header in the 94th minute, just 13 minutes after entering the fray, proved enough to turn a dour stalemate into a crucial three points.
Tony Popovic's side were coming off three consecutive losses and hadn't won in the A-League Men since Boxing Day amid poor results and postponements, with Saturday night's result lifting them back into the top six.
But their win was soured by a first-half quad injury to defender Matthew Spiranovic.
The Mariners are now winless in five ALM games, with their last league victory on December 18, after once again dropping points by a goal conceded in the 90th minute or later.
Popovic stuck with under-fire goalkeeper Ivan Kelava, who saw Central Coast's Marco Urena put the ball in the back of the net in the 14th minute, but he was offside.
Jake Brimmer turned Marco Rojas' flick-on home in the 26th minute but had strayed into an offside position and after a prolonged VAR referral, the offside ruling was upheld.
Rojas had a 55th-minute penalty shout waved away while Central Coast had back-to-back chances from Josh Nisbet and Jason Cummings in the 60th minute deflected and blocked away.
Victory seized control when Velupillay came on in the 81st minute.
Five minutes later, Velupillay, slipped through Francesco Margiotta, only for the Italian to fire wide.
Less than two minutes later, Robbie Kruse burst forward and found Chris Ikonomidis, who rolled the ball across the face but no-one was on hand to tap home at the back post.
Victory found their equaliser when Ikonomidis stood up his defender, then lofted a ball to the back post where Velupillay rose highest to head home the winner.
