However, the home team made heavy weather of seeing off the newly promoted Gretna.
It was not until two late goals from Carlos Cuellar and substitute Jean-Claude Darcheville that Rangers could finally relax.
In a flat first half Gretna threatened as much as Rangers, yet the visitors found themselves unjustly behind at the interval.
The goal was typical of a subdued first-half performance by the home team with Kris Boyd's shot, from a short free-kick from Barry Ferguson, being deflected past Greg Fleming in the Gretna goal.
It was almost Rangers only attack of the half and came about after a clever turn by Daniel Cousin on the edge of the box led to a foul by Aurelien Collin.
Gretna were by no means overawed and the Uruguayan Fabian Yantorno was always looking dangerous and tested Allan McGregor on a couple of occasions.
Rangers were slack at the start of the second half when Yantorno received a quickly-taken free kick and was allowed to advance unchallenged before curling his shot narrowly over.
The visitors went even closer when Colin McMenamin held off the challenge of Cuellar, but McGregor saved bravely at the forward's feet.
Gavin Skelton had to be alert to deny Boyd after the striker played a quick one-two with Cousin at the edge of the area and Ferguson headed Alan Hutton's cross just wide as Rangers finally woke up.
Yantorno created panic in the home defence with a curling free-kick which dropped on the six-yard line and led to an almighty scramble before Cuellar eventually cleared.
Rangers secured the crucial second goal from a set piece move. DaMarcus Beasley 's deep corner found Andy Webster rising high above everyone to bullet his header into the roof of the net despite Fleming getting a hand to it.
Not to be outdone his co-central defender Cuellar did likewise.
Darcheville was fouled by Abdul Osman and from the resultant free-kick by Ferguson, Cuellar headed powerfully home.
It was all over for Gretna and their heads went down even further when the powerful Darcheville cut past Skelton, before firing in a shot from the by-line which appeared to take a deflection past the helpless keeper.