A goal in the last minute by substitute Dean Shiels flattered the visitors who rarely tested Allan McGregor in the Rangers goal all afternoon.
A well-taken goal by Jean-Claude Darcheville just before half-time put the home side ahead and when substitute Nacho Novo scored with 11 minutes to go it was all over for the side from the capital.
A turgid first half was only enlivened by Carlos Cuellar's clearance from Filipe Morais' cross while Sasa Papac shot narrowly over the bar but they were about the only incidents of note other than Rangers' opening goal.
The goal itself was not in keeping with the rest of a poor half as it was well-constructed and taken.
Papac's pass inside Martin Canning left the wing-back stranded and Darcheville cut in from the left before curling a powerful shot high past Yves Makaba-Makalamby.
Rangers pushed forward at the start of the second half seeking to add to their lead. Steven Davis' superb pass found Darcheville clear on goal but Makaba-Makalamby managed to block his shot.
The Hibs keeper was again alert when he raced from his goal to beat Darcheville to another superb Davis throughball.
Rob Jones did well to prevent Darcheville reaching Papac's dangerous cross before Rangers scored their second.
Barry Ferguson's short pass found Davis and, from his deep cross, Chris Hogg lost control allowing Novo to latch on to the loose ball and drill his shot low past the keeper.
To their credit Hibs kept pushing forward and substitute Shiels volleyed home after his initial effort had come back off the crossbar.