The home side looked sharper than Hibs in the opening stages and they were first to the ball in the middle of the park.
Rangers thought they had taken the lead after 15 minutes but Dado Prso's strike was ruled out for offside.
However, they did not have to wait long to take the lead as Prso opened the scoring 60 seconds later. Following a strong run by Nacho Novo, the tiny Spaniard picked out Prso who fired home with ease.
Rangers deservedly doubled their lead after 32 minutes. Charlie Adam crossed the ball in from the left and Libor Sionko fired the ball home at the back post.
Prso almost added a third 60 seconds later when he turned on the edge of the area before seeing his shot well saved by Zbigniew Malkowski.
Barry Ferguson added a third goal as Rangers threatened to run up a cricket score. Adam floated a cross into the box and the skipper was in acres of space to head into the net.
Hibs had an excellent chance to pull a goal back before the break but Chris Killen contrived to fire wide from close-range.
Hibs manager John Collins made two changes at the break and the visitors started the second half well but they were reduced to ten men when Ivan Sproule picked up a second booking for petulantly throwing the ball away.
Rangers were still dangerous on the break and substitute Filip Sebo went close to extending their lead before the end of the match.