In a first half of few chances, Andy Ryan came closest to breaking the deadlock for the visitors as he forced Andrew Mills into a smart save down to his right midway through the first half.
Just as it looked like both sides would be going in level at the break, the deadlock was broken in the first half added time.
A neat Glentoran move saw Pat Hoban tee up Palmer with a tidy flick, with the midfielder taking one touch before striking back across goal into the bottom corner with Rohan Ferguson rooted to the spot.
The Glens resumed the second half much like they did the first, with real intensity and fight without creating anything meaningful in regards to clear cut opportunities.
As the game made its way into the final 15 minutes, the Inver Reds drew level through Ryan who tapped home from a few yards out after substitute Conor McKendry found him inside the six yard box with a pinpoint square ball.
The hosts were reduced to 10 men just minutes before full-time, with Kamson Kamara sent for an early shower for a second bookable offence.
Larne were determined to make their one-man advantage tell in extra-time, but couldn’t find a winner meaning penalties would determine the outcome of the Irish Cup quarter-final clash.
Ferguson was the hero for Larne, saving three penalties to send the Inver Reds racing into the semi-finals.
