The visitors squandered a two-goal lead in the second half as Junior Morias lived up to his iconic chant and inspired the Buddies with two goals.
After an arduous opening 10 minutes was played amidst terrible conditions, Livingston silenced the home support by opening the scoring through Aymen Souda.
Jim Goodwin adopted a 4-4-2 formation and it paid dividends when his two strikers combined beautifully to equalise in the 31st minute.
The imposing Obika robbed Ricki Lamie of possession on the edge of the box before squaring the ball across goal for his striker partner Morias to tap home from close range.
The visitors edged the first-half and they deservedly went back in front on the stroke of half-time. The Saints had been warned about Craig Sibbald's excellent delivery earlier in the game but they failed to deal with his in-swinging free-kick again as Jon Guthrie rose highest to head past Hladky.
Livingston introduced captain Alan Lithgow at the break as they reverted to their familiar back three to combat the hosts' physical strikers but they doubled their advantage on the hour.
It was horrendous defending from St Mirren as they failed to deal with a long ball which allowed Souda to nip in before flicking it over a defender and placing a composed finish past Hladky.
St Mirren refused to accept defeat and after Tony Andreu's cross come shot bounced off the deck, Buddies top scorer Obika prodded him from close range.
Cooke's presence troubled the Livi defence and fellow sub Andreu gathered the ball before cutting the ball back for Obika to loop a deflected shot over the despairing Sarkic to draw the Buddies level.
Both sides persevered to find a winner to little avail although Scott Robinson was booked for simulation late on as he claimed for a penalty.