Stuart McCall’s side progressed to the two-legged final, the winner of which will secure a place in Scotland’s top-flight next season, after prevailing 2-1 on aggregate thanks to their 2-0 win over at Ibrox in the first leg in midweek.
The home side were unable to take advantage of an impressive start to the match when they pegged Rangers back, but they rarely threatened to make the breakthrough and had only a stoppage-time goal from Jason Cummings to show for their efforts.
Hibs had a penalty claim waved away by referee John Beaton when the ball came up against the outstretched arm of Dean Shiels with just four minutes on the clock, but the Rangers striker was unable to get out of the way of the ricochet from Dominique Malonga.
Liam Fontaine then got in front of Marius Zaliukas to meet a corner from Scott Allan but sent his header over the bar.
Hibernian continued to press and Fraser Fyvie tested Cammy Bell with a low drive from 25 yards before Cummings flicked the ball over Zaliukas and forced the ‘keeper into another diving save a minute later.
Cummings had another opportunity when he got in behind the Rangers defence to run on to an Allan flick, but dragged his shot wide from 15 yards.
The visitors finally created a chance on 24 minutes when a brief spell of pressure around the Hibernian penalty area ended with Kenny Miller shooting weakly at Mark Oxley.
And 90 seconds later Miller got in front of Paul Hanlon to meet a Ricky Forster cross but could not divert his header on target.
Nine minutes before the break Lee Wallace lost possession in the middle of the pitch and Allan burst forward to slip a pass to Malonga but his shot from inside the box was poor and easily saved by Bell.
At the other end Haris Vuckic came close with a curling shot from 25 yards which Oxley pushed round the post, seconds after he clashed with Liam Craig while trying to get past the Hibs midfielder.
Bell had to be alert to take the ball off David Gray’s head at the back post after Allan chipped the ball in from the left side of the penalty area in the opening minutes of the second half.
Malonga crashed a volley a couple of yards wide from 12 yards after Craig chipped another cross from the Hibs left three minutes later.
And Bell made a terrific save when he got down to his left to turn a powerful drive from Malonga round the post.
Vuckic did pick up a yellow card when he threw himself down in the Hibernian penalty area in an attempt to win a penalty with 20 minutes remaining.
Hanlon had an effort hit the outside of the post in the last minute of regulation time, but three minutes later Cummings netted with a delightful chip from 16 yards.
Hibernian’s hopes of getting a final chance ended when Beaton blew the final whistle, but the home side had left it too late and Rangers progress on a 2-1 aggregate score.