In the opening few minutes, a mix-up in the Bangor defence gifted Paul O'Neill an opportunity, but the striker fired wide.
Larne then had another chance to break the deadlock on 16 minutes with both Matt Ridley and Dan Bent having efforts blocked before the Seasiders eventually cleared their lines.
As the half progressed, chances grew few and far between with Ronan Doherty and Tiarnan Mulvenna both having efforts saved at either end.
Gary Haveron's side then believed the visitors should have been reduced to 10 men when Matty Lusty's run through on goal was cut short by Alfie Mitchell. However, Steven Gregg cautioned the defender.
Rohan Ferguson was called into action to thwart Jay Boyd's effort before Doherty came close once again in the final minutes of the first half.
It was a slow start to the second half with neither team having a chance until the 62nd minute when Patrick Solis Grogan made a great save to tip Sean Graham's effort over the crossbar.
Haveron then turned to his bench and brought on Mark Randall in an attempt to spark the match to life.
The experienced midfielder nearly made an instant impact when he fired towards goal, only for his shot to be deflected wide with Matt Ridley unable to fire home the resulting corner from the back post.
Larne broke the deadlock when Sloan‘s left-footed strike from 25-yards out flew past Solis after good build-up play from the home side.
Shortly after, Sloan had another go from a similar distance but could not find the top corner in style once again.
Larne now face Portadown on Saturday, while Bangor travel to the Oval to play Glentoran as their wait for their first win of the season continues.