Kemar Roofe, who had come on for Alfredo Morelos midway through the second half of a tense and frantic contest, proved to be the match winner as he converted an 85th minute penalty awarded for a Ryan Porteous foul on Ryan Kent.
Van Bronckhorst had been poised to also introduce forward Fashion Sakala from the bench in a bid to break the stalemate but then opted to send on midfielder John Lundstram to see out the victory which puts Rangers seven points clear of Celtic at the top of the Premiership table.
“There needs to be competition in any team and any squad,” said van Bronckhorst. “I have to pick my 11 and also change the game with my subs. That is my role, to see what the team needs at moments of the game.
“I wanted to bring on Sakala and then we got the penalty and I switched to Lundstram. Those are the moments when you have to decide and I think I decided well.”
It’s now three wins out of three for van Bronckhorst since taking charge of the Scottish champions and he recognised the significance of a result which sees them retain the initiative in the title race ahead of the clash between their closest pursuers Celtic and Hearts on Thursday night.
“It was a very big win,” he added. “It was a tough game as we expected before kick-off. There was a lot of physical play from both teams and not many chances. But we’ll take the win and it’s three more points for us.
“The game was decided by transition moments. In the first half, we had some good moments to score. There was a great chance for Alfredo Morelos.
“In the second half, you could see when we won the ball we had the spaces to attack. However, we weren’t too sharp in those moments and we gave a lot of loose balls away.
“So we had those transition moments to defend as well. But those moments were there for both teams but luckily for us we came away with the win.
“It’s always good to come to places like Hibs (and keep a clean sheet). It’s a tough opponent and they’re a good side, very well organised. So to keep a zero here is massive for us because we knew we would always get chances.
“Today we scored from a penalty and after that we controlled the game with the substitutions. I put in Lundstram so defensively after that we were very solid. I am very pleased with the win.”
Roofe, who returned from a three-match injury absence to score his 10th goal of the season, admitted he and his team-mates were motivated by their desire to make up for their 3-1 defeat against Hibs in the Premier Sports Cup semi-final at Hampden 10 days earlier.
“Of course (we had a point to prove),” said Roofe. “That is what football is about. They did us in the semi-final and it hurt us a lot. So it was important for us to get the three points today.”