It was yet another strong display from the Light Blues in the competition as they defeated the Bundesliga side 6-4 on aggregate over the two legs.
James Tavernier netted a first-half penalty, before Jude Bellingham and Donyell Malen had the visitors ahead at the interval before the captain was again on target to draw Rangers level in the second-half.
Giovanni van Bronckhorst named an unchanged side from last week’s victory in Germany as Rangers started with a back five of Allan McGregor in goal with James Tavernier, Connor Goldson, Calvin Bassey and Borna Barisic in front of him.
John Lundstram, Ryan Jack and Joe Aribo were in the middle of the park, while Scott Arfield and Ryan Kent provided support to Alfredo Morelos.
With just two minutes on the clock, Rangers were awarded a free-kick in a dangerous position just to the right of the box. Captain James Tavernier stepped-up to the set piece and whipped an inviting ball into the box which Alfredo Morelos managed to get his head to but it was just off target from the Gers striker.
It was a lively start at Ibrox and the visitors almost had a goal with only the post denying them in the fourth minute. The ball broke for Jude Bellingham inside the box and his shot bounced back off the woodwork before Hummel’s effort was blocked by the Light Blues.
Malen came close for the visitors around the 20 minute mark as he turned on the edge of the box before drilling a powerful strike towards goal which flashed wide of Allan McGregor’s right-hand post.
It was Rangers who took the lead just a few minutes later as the referee pointed to the penalty spot after Ryan Kent was fouled in the box.
Scott Arfield had initially won the ball back on the right before a good passage of play between Alfredo Morelos and Joe Aribo saw it played into the path of Ryan Kent on the left. Kent cut inside the box before being taken down by Julian Brandt as the Spanish official pointed to the spot.
Captain James Tavernier stepped-up to take the penalty and calmly slotted beyond Gregor Kobel to raise the roof on a sold-out Ibrox and give Gers a three goal aggregate advantage against the Bundesliga side.
Moments later, Brandt almost instantly made up for conceding the penalty at the other end but Allan McGregor was equal to his shot to block the effort.
The visitors were level in tonight’s second-leg on the half-hour mark, Connor Goldson’s block on a Donyell Malen shot fell into the path of Jude Bellingham and the England international fired beyond Allan McGregor.
At the other end, Rangers had a fantastic chance to go back in front as Joe Aribo played in Scott Arfield as he drove into the box but Kobel managed to block his low shot before the rebound fell to Alfredo Morelos and his shot was cleared off the line, before Allan McGregor was again called into action as he tipped wide a Donyell Malen strike.
Dortmund took the lead at Ibrox three minutes before half-time as Malen got on the scoresheet. Jude Bellingham guided the ball into the path of the striker and he managed to touch beyond McGregor to reduce the aggregate deficit to just one goal.
Giovanni van Bronckhorst named one change to his side at half-time as Leon Balogun came on in place of Borna Barisic, with Calvin Bassey moving from centre-back to left-back.
Rangers had a chance early in the second-half as Alfredo Morelos beat the offside trap to race towards goal, he cut in from the right to get a shot away but it was deflected just wide.
It was a strong start to the second half for van Bronckhorst’s men and Morelos had another opportunity as Ryan Kent’s effort was blocked with the rebound falling for the Colombian as he turned just inside the box but his strike was saved by Kobel.
Ibrox erupted once again as James Tavernier scored his second of the evening to restore the Light Blues’ two-goal aggregate advantage. Calvin Bassey’s ball from the left fell for the Rangers captain and he struck it first time into the back of the net to draw Rangers level in this second-leg.
Shortly after The Light Blues thought they had taken the lead as Alfredo Morelos won the ball just inside the Rangers half to break through on goal before playing in Ryan Kent who found the back of the net. However, after a VAR check the goal was disallowed for a foul in the build-up.
Into the final 10 minutes as Dortmund searched for a route back into the match, the two substitutes combined as Steffen Tigges cross met the head of Youssoufa Moukoko but he couldn’t keep his effort down as it drifted over the bar.
It was another strong display from the Light Blues who will find out their last 16 opponents tomorrow.
RANGERS: McGregor, Tavernier, Goldson, Bassey, Barisic (Balogun, 46), Lundstram, Jack, Aribo, Arfield (Kamara, 69), Kent, Morelos.
SUBS: McLaughlin, McCrorie, King, Davis, Sands, Lowry, Amad, Wright, Roofe, Fashion Jr.
BORUSSIA DORTMUND: Kobel, Can, Hummels, Schulz, Hazard (Reinier, 69), Bellingham, Dahoud, Meunier (Wolf, 46), Reus (Witsel, 86), Brandt (Moukoko, 69), Malen (Tigges, 76).
SUBS: Unbehaun, Hitz, Guerreiro, Passlack, Pongracic.
Referee: Antonio Mateu Lahoz