The Highlanders, now seven games unbeaten, moved up a place to sixth with their 1-0 win after the pacey Irishman’s dramatic impact from the bench.
Dubliner Mulraney was immense in his 21 minutes on the park on an evening otherwise bereft of inspiration.
But the hosts’ play-off chances remain very much alive.
It was a dreich night, sodden underfoot, with a stiff breeze making life difficult for the players.
Falkirk settled first with early pressure bringing a free-kick which Sean Welsh swirled under the crossbar only for home keeper Mark Ridgers to clutch confidently.
But the hosts found some fluency and, after 15 minutes, Falkirk only just escaped with Liam Polworth’s corner headed against the bar by Gary Warren.
Austin followed in quickly but Paul Watson was sharp to volley off the line.
Reghan Tumilty was a lively outlet on the right flank for Falkirk and his cross set up Tom Robson just before half hour only for the ex-Sunderland wing-back to take a heavy touch.
Falkirk were brighter after the break, and it took a clearance off the line by Carl Tremarco after 63 minutes to thwart a Watson header.
Home manager Robertson made a double change with his team beginning to tire after 69 minutes.
Irish wingers Aaron Doran and Jake Mulraney replaced Austin and Charlie Trafford as the hosts threw more bodies forward.
Mulraney’s pace turned the heat on Falkirk, forcing keeper Conor Hazard to race outside his box for a tackle. Brad Mckay’s cross was hacked clear by Aaron Muirhead.
Moments later, Tremarco fired just over after another Mulraney delivery.
Oakley then headed into the net from a Polworth cross, but Caley Thistle’s breakthrough came with eight minutes left.
Mulraney jinked past several Falkirk challenges and then hammered a low 16-yard strike past Hazard.
Home keeper Ridgers spared his team, an equaliser with a brilliant 90th minute save from Jordan McGhee’s header.