In the opening few minutes of the game, Paul O'Neill had a good chance to break the deadlock after Doherty's shot deflected into the path of the striker, but he could not keep his effort on target.
At the other end, Owen Wardell and Elliot Dunlop both fired just wide as both sides continued to push for the opener.
Shea Callister was then forced to make a good save to gather Leroy Millar's effort from a James Simpson pass.
Larne took the lead in the final 10 minutes of the half when Doherty's strong left-footed finish struck the crossbar and found the back of the net.
The Inver Reds doubled their lead on 52 minutes after McEneff fired home Simpson's cross from the left wing.
The Crues pushed for a quick response and thought they had found one when Jacob Blaney headed home Donal Rocks' cross, but he was offside.
In the 75th minute, Gallagher was shown a straight red card for a late tackle on Elliot Dunlop before Larne's assistant manager Mick O'Boyle was also dismissed for his reaction to the decision.
Despite being down to 10 men, Larne extended their lead on 89 minutes when O'Neill played the ball across the box for Sandiford to fire home with his first touch of the game.