The Gers boss was without Ianis Hagi, Ryan Kent and Alfredo Morelos due to injury, suspension and international duty respectively with Joe Aribo in the stand after coming back from the African Cup of Nations following Nigeria's departure. Steve Davis, Filip Helander and Leon Balogun were also out.
Fit-again Scott Arfield and Ryan Jack, as well as recently returned Kemar Roofe started on the bench, while 18-year-old midfielder Alex Lowry made his first start after scoring as a substitute against Stirling Albion in the Scottish Cup last Friday night.
On a wet and wild night at Ibrox when the cinch Premiership leaders came up against a well-organised Livi side, van Bronckhorst called upon Arfield, Roofe and Jack in the second half.
Arfield, featuring for the first time since Boxing Day, scored the only goal 15 minutes from time to keep Rangers four points clear of Celtic at the top of the table but the Dutchman is pleased to have more choices for Dingwall.
Van Bronckhorst, who will have new Manchester United loan signing Amad Diallo available for Saturday, said: "It was very difficult circumstances to play in those conditions against a team who did very well, made it very compact and we couldn't play the game we needed against this opponent.
"It was difficult to control the ball, pass the ball in the wind but in the end we created enough chances to score goals but we only scored one which made us the winner, which is the most important thing.
"I am really happy that I could sub Scott Arfield because we know how important he is to the team.
"We put him in for the last 30 minutes, the same as Kemar, and of course Ryan Jack is back as well so the squad is getting back to full fitness.
"Players are coming back and of course for the weekend we have players back, especially Ryan Kent and Joe and I have Alex of course so I have more choice.
"So this win is very important for us. We can work hard with a bigger squad for the next fixture."
Midfielder Lowry turned in another fine performance but van Bronckhorst revealed the teenager had to overcome early nerves after first coming in to train with the first team squad.
Explaining why the youngster had made the breakthrough, he said: "Of course it’s his talent. His confidence was always there.
"I think the first session he joined he was a bit nervous. You could tell. He was making a lot of mistakes actually in things he can do well.
"You could see he can control the ball well, he can pass it. But at first he made many mistakes in that.
"But after when he was a little bit more settled you saw his confidence coming back.
"You could see the Alex you see now on the pitch with moments where he’s very dangerous and very energetic and creating dangerous chances.
"At times you also saw his youthfulness when he had to play faster but that’s a normal process for him.
"I’m really pleased for him with the way he’s performing now. We have to make sure we keep pushing him to become better.
"Of course he’s playing because we are missing a lot of players but he also plays because he has the ability to play.
"Now with Joe and Scott back, the competition is high but he has to go on and play like this and we will see in which games we will give him the chance to get minutes."