Rangers will meet Motherwell in the Scottish Premiership play-off final despite a 1-0 defeat at Hibernian on Saturday.
Stuart McCall's men headed to Easter Road with a 2-0 advantage from the first leg, with Nicky Clark and Kenny Miller having found the net at Ibrox on Wednesday.
And Rangers did a sterling job of protecting their lead in Edinburgh against the Championship runners-up, with their hosts piling on the pressure in the opening 20 minutes.
That threat eased as the match progressed, but Paul Hanlon hit a post in stoppage time before Jason Cummings curled in a late consolation.
"We knew we'd be put under the cosh and a fourth game in 12 days was always going to be difficult," McCall told BBC Scotland. "But, to a man, we got stuck in and defended well. They all did a shift.
"The fans kept us going for the final 25 minutes because that's all you could hear.
"I was disappointed to lose a goal in the last minute. Thankfully, it wasn't five minutes before because I don't think we could have coped with extra-time; too many tired legs, tired bodies."
Rangers and Motherwell now clash over two legs - the former looking for a return to the top flight with a third consecutive promotion.
Motherwell were already assured of their place in the play-off prior to Saturday's last round of fixtures in the Premiership's bottom half - Ian Baraclough's men playing out a goalless draw at home to Partick Thistle.
"We've already started preparing [for the play-off against Rangers] and we've watched them five or six times at Ibrox," said Baraclough. "We'll go to Ibrox with belief that we can give them problems."
Hamilton Academical rubbed salt in the wounds of already-relegated St Mirren with a 1-0 win, while Ross County came from behind to win 2-1 at Kilmarnock.
