Alex McLeish's side recorded a 4-1 win over SPL bottom side Livingston, but for much of the second half at least the home side were really tested by Paul Lambert's troops.
Rangers eased ahead in the early stages with the opening goal coming from new striker Kris Boyd on eight minutes.
Peter Lovenkrands' shot from a Robert Malcolm free-kick was deflected and the former Kilmarnock frontman was on hand to put the ball past Roddy McKenzie.
Lovenkrands and Thomas Buffel tested McKenzie again and again but couldn't add a second for Rangers before the interval.
Livingston's sole response in a poor first half showing was a Steve Hislop effort straight at Ronald Waterreus on 17 minutes.
After the break the visitors forced themselves back into contention when Gabor Vincze leveled on 52 minutes. The ball broke to him after Marvin Andrews failed to clear and he sent a powerful drive past Waterreus from 12 yards.
Rangers, however, were back in front soon after as Barry Ferguson found Buffel who in turn found Boyd and he shot low into the corner of the goal for his second of the game.
Andrews should have made it 3-1 with his header from a Lovenkrands corner on 62 minutes and Vincze headed into the side-netting at the other end a couple of minutes later.
Dado Prso and Nacho Novo replaced Lovenkrands and Boyd upfront as Prso notched another couple of goals for Rangers before full-time to seal the win.
On 89 minutes and after winning a free-kick, Prso passed the ball beyond McKenzie from 18 yards.
Then in stoppage time he raced through on goal and slotted past McKenzie to complete the scoring.