The away side made a bright start with Ronan Wilson and McGonigle having good chances in the opening five minutes.
In the seventh minute, Limavady thought they had opened the scoring when the in-form McGonigle's powerful effort from the edge of the box found the top corner.
However, he was adjudged to have been marginally offside and the goal was chalked off.
As the half progressed, Glentoran began to dominate with Jack Malone unable to get the connection needed to steer home Ross Clarke's flick before Martin Gallagher was called into action to gather Clarke's curling shot.
The lively McGonigle continued to look a threat and, in a cagey closing 10 minutes of the half, his effort sailed just wide.
At the break, McCourt brought on striker Pat Hoban for his first league appearance since the opening game of the season.
However, the substitution did not have the instant impact that the home side desired, with chances to make the breakthrough few and far between.
In the only real opportunity in the opening 20 minutes of the half, McGonigle's free-kick forced Mills to make a comfortable save.
Hoban's header was then gathered by Gallagher before fellow Glentoran substitute Gallagher fired well over the crossbar.
The Glens secured the victory in second-half additional time when Gallagher's well-timed corner found the unmarked Larmour, who steered home from close range for his first goal of the season.