The midfielder was on hand to score the rebound after skipper James Tavernier saw his first half penalty saved by David Marshall before Fabio Silva sealed the win.
It was the second time he has been on the scoresheet this season after also grabbing a goal in the win over Dumbarton earlier in the campaign.
The playmaker knew it was going to be tough just three days after the 2-2 draw with Benfica and he was thrilled to make the last four.
Speaking to Rangers TV, he said: "It was nice to get on the scoresheet, it is another one in the cup, I wish I had one in the league.
"It was good to score. It was hostile and that's what you want to play in front of.
"It was a tough game and I don't think we played our best game, but the pitch wasn't great.
"The most important thing is getting through. Hibs had a right go to be fair to them but it is job done and into the next round.
"It's been a tough week but that comes with success. When the club is doing well then you have this amount of games.
"We are into the last 16 in Europe, the Cup semi-final, so that is what the squad is for.
"We have to keep going.”
Birthday boy Jack Butland kept another clean sheet - to secure a return to Hampden for the Gers.
Lundstram was full of praise for the keeper and back four and believes it gives the squad confidence in every match.
He added: "We have been great at the back all season and I don't know how many clean sheets that is now, but that gives us a solid base to work from.
"It wasn't pretty but we know if we have that base defensively then we can always score goals, we have such a threat up top.
"I am looking forward to the draw now to see who we get and it will be another test to overcome."