Following the 0-0 draw in Piraeus, NEC were initially deemed the favourites but were beaten 2-1 by lowly Telstar at home last weekend. Olympiacos, meanwhile, had a week's rest with the Greek Super League not starting until Saturday, August 22nd.
NEC were the slightly better team in the opening 30 minutes, but both teams were hit with injury issues early - Olympiacos forward Jota Silva was forced to retire with a hamstring injury, while NEC's Sami Ouaissa and Philippe Sandler were unable to continue.
After a passive first half, poor defending from NEC cost them dearly in the first minute of the second half, with Ayoub El Kaabi tapping in a rebound to give the Greeks the upper hand.
It took over an hour for NEC to show real signs of life, with Emre Mor testing Balsa Popovic from distance a minute before Bryan Linssen nearly beat Popovic from up close, with the Montenegrin stopper keeping NEC goalless with his feet.
It was the 35-year-old Linssen who made the Goffertstadion erupt, converting on a sublime Dusan Tadic cross to score NEC's first-ever UEFA Champions League goal.
NEC's momentum continued when Olympiacos were shown a red card - Konstantinos Fortounis planted his studs on the ankle of Darko Nejasmic, prompting referee Maurizio Mariani to change the yellow into a red card and leave the Greeks down a man for the last 10 minutes and potentially extra time.
Substitute Kaj Sierhuis set Nijmegen momentarily alight with a 93rd-minute goal, heading in a sharp cross from Emre Mor. The Turkish former wunderkind was eventually the reason the goal was cancelled, with Mor standing centimetres offside in the build-up to the goal.
An emotional Mor vindicated himself five minutes into extra time, thumping the ball into Popovic's goal to send Nijmegen into a frenzy and give his side the lead after all.
NEC kept up the pressure following Mor's goal, with youngster Kevin Kers coming closest to a game-sealing goal. The energy was flowing out of Olympiacos, who were no longer able to put up a valiant fight with minutes to go before the full-time whistle.
Emre Mor's extra-time goal wrote history for NEC, who captured their first UEFA Champions League win in club history. In the play-offs for the League Phase of the UEFA Champions League, NEC will face last season's surprise package Bodo/Glimt from Norway.
Check out the full match statistics on Flashscore

