Djeidi Gassama, for the second time in the tie, came up with a huge moment as he cancelled out Filip Duricic’s goal in the second-half to see Rangers to a 3-1 aggregate victory.
From last week’s first-leg, Russell Martin named an unchanged line-up with Jack Butland starting in goal behind a back four of James Tavernier, Nasser Djiga, John Souttar and Max Aarons. Joe Rothwell, Nico Raskin and Mohamed Diomande were in midfield, while Findlay Curtis and Kieran Dowell supported striker Danilo.
For Panathinaikos, there was just one change with the suspended Georgios Vagiannidis replaced in the starting line-up by Giannis Kotsiras.
It was the home team who got the match under way at Athens Olympic Stadium, and Rangers had a few corners to defend early as Panatinaikos looked to put pressure on and get themselves back into the tie.
Their first real chance came as a headed clearance from inside the Rangers box fell for Tasos Bakasetas and he released a left-footed strike towards goal but it was just wide of Jack Butland’s post.
Minutes later, Butland had to block a shot from a tight angle from captain Fotios Ioannidis in what was a lively start for the home side.
The Rangers number one, who produced some fine saves in last week’s first leg, was called into action once again as Facundo Pellistri got the better of Max Aarons on the right-flank and raced through on goal but Butland was strong to block the low effort.
Facundo Pellistri sent a dangerous cross into the box with 20 minutes played, finding Fotios Ioannidis in a central area and he glanced a header towards goal but it was blocked by Butland.
It had been difficult for Rangers to find moments to attack in this tie so far, but a corner on the 30th minute opened up an opportunity. Joe Rothwell’s corner was headed back across goal by John Souttar and fell for Findlay Curtis but he could only turn it wide.
Another corner provided a chance with five minutes of the first-half remaining as Joe Rothewell delivered a superb ball into the box, which Raskin managed to get his head to but it looped just high of the target.
The home side had the ball in the back of the net with 52 minutes played, Tasos Bakasetas delivered a cross in from the right, and Filip Duricic had made a run in at the back post and managed to get enough on it to turn it behind.
The goal prompted an instant change from Russell Martin as Djeidi Gassama entered the field in place of Findlay Curtis.
It took the winger no time to have a crucial impact as he restored Rangers two goal advantage on the hour mark. Nico Raskin made ground down the left, before Danilo saw two efforts blocked by the keeper.
The second clearance fell for Djeidi Gassama and it was a superb strike as he guided a right footed shot into the back of the net.
Fotios Ioannidis came close again with an effort from inside the box, before Ahmed Touba released a powerful strike from distance which curled just wide of Butland’s right-post.
There was a huge chance in the final stages of the match as Cyriel Dessers was through on goal but the goalkeeper pulled off a good save to deny the Rangers striker.
RANGERS: Butland, Tavernier, Djiga, Souttar, Aarons, Rothwell (Bajrami, 82), Raskin, Diomande, Dowell (Jefte, 73), Curtis (Gassama, 57), Danilo (Dessers, 82).
Subs: Kelly, Cortes, Barron, Cameron, Fernandez, Gentles, Rice, Hutton.
Panathinaikos, Dragowski, G. Kotsiras (Cerin, 66), Palmer-Brown (Swiderski, 78), Touba, Kiriakopoulos, Bakasetas (Tete, 66), Chirivella, N. Maksimovic, Pellistri, Duricic, Ioannidis.
Subs: Lafont, Kotsaris, Ingason, Mancini, Jedvaj, Mlandenovic, Fikaj, Jeremejeff, Brejou.