Rangers embarked on the long journey south with bruises and a sense of frustration, but also a renewed air of conviction.

There was little virtuosity in the way they overcame Peterhead, and more than a few tackles that left visiting players nursing pain and grievances. Even so, Rangers could take something meaningful from increasing their commanding lead at the top of the Irn-Bru Third Division, as the victory was a reminder that this team, while still nurturing its potential, has learned how to cope.

The mood was one of satisfaction, at least enough for the manager, Ally McCoist, to joke that the advertising hoarding into which Ian Black was sent careering by Dean Cowie, the combative Peterhead midfielder, would be "out for three weeks", and that Francisco Sandaza was "just one of those unfortunate guys" when caught by a boot in the face. He may have a broken nose.

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The Spaniard said that "the referees should watch the tackles", but his manager was more concerned with how his men coped with the physical challenge of Peterhead.

"Big boys get on with it," he said, and once Sandaza opened the scoring, and Peterhead were reduced to 10 men, it was a case of seeing things out.

This encounter was a measure of Rangers. They were back to where it all began, since the Ibrox side's first game in the third division was at Balmoor Stadium. That was on a summer's day, when the occasion could still best be understood as a novelty, something that had to be borne. It was also a lesson for Rangers, though, in the rigours and the realities of life in the bottom tier being bluntly revealed.

Rangers needed a late equaliser to salvage something from that first exposure to the third division. It took several months, and further setbacks in away games, for the team to come to terms with their circumstances. All had to deal with the biting wind, but in the way Ross Perry and Emilson Cribari coped with uncompromising nature of first Rory McAllister then the brawny Martin Bavidge, Rangers displayed their own steel.

"If our two centre-halves don't fancy it then we're bang in trouble," McCoist said. "The two of them handled the natural enthusiasm and aggression of the Peterhead forward line, and Kyle Hutton had his best game for Rangers. But our decision making in the last 20 minutes was poor and our finishing, again, isn't at the level it should be. We were carrying a little bit of luck."

The goal came from one of Rangers' more dynamic moves in the first half, with Lee Wallace and David Templeton playing a one-two before the former drove a shot that Graeme Smith, the Peterhead goalkeeper, could only bundle away.

Sandaza, displaying sharp instincts, followed in to calmly tuck the rebound in the net for his first goal since August.

"He got his rewards," said McCoist. "It was a great goal, really well worked, and he deserves it for the work he's doing. I'm sure the goal will give him the confidence and open the door for him to score a few more."

Peterhead were dogged, and McAllister was always willing to harry and chase. It was a bitterly cold afternoon – and some home fans warmed up by doing a conga behind one of the goals – but there were occasional moments of hopefulness for the home side, at least in the first half, with McAllister seeing a header saved at close range, and David Cox shooting just wide. Once McAllister was sent off after the break, though, when a handball prompted Mike Tumilty to show the striker a second yellow card, Peterhead were restricted.

"I'm disappointed that we didn't finish with 11 men," said Jim McInally, the Peterhead manager. "Listen, I've got a lot of history with that referee, he's done me a lot of damage before, so I wouldn't give him the pleasure of talking about him. It happens a lot and you don't get booked, and when you've been booked already a lot of referees turn a blind eye to it rather than spoil the game."

Peterhead remained sturdy and tough opponents, with Cowie targeting Black for head treatment on occasion, but Rangers withstood the pressure. They ought to have scored twice before the end, too, but Templeton shot wide and then over from good positions. In the end, though, the victory was ground out.