The Scottish champions reinforced their position at the top of the Premiership table with a 3-1 win over Livingston at the Tony Macaroni Arena.
But it wasn’t entirely straightforward for Rangers as, after early goals from Scott Arfield and Joe Aribo put them in command, they were pegged back by Bruce Anderson’s goal for Livingston.
It wasn’t until substitute Fashion Sakala headed home in the 78th minute that van Bronckhorst felt able to relax and savour his second win in two matches in charge after last Thursday’s 2-0 Europa League victory over Sparta Prague.
“I think we controlled the game,” said van Bronckhorst. “We had a great start in the first 20, 25 minutes and scored two goals. We knew the chances would come with Scott in that manner and making his runs into the spaces.
“The first goal was excellent, the second goal was also really good - good positional game from us and a great shot by Joe. I think after that we lost a little bit of the intention of playing and also the speed of play.
“We were a bit sloppy and of course the 2-1 made it a real game. In the second half we controlled it more, we didn’t give any chances away. If you control so much of the game you need to make sure you finish the game as early as possible and we kept Livingston too long in the game.
“When Sakala scored from the corner kick it was a relief for us because it was 3-1 and after that we kept the ball and didn’t give any chances to play anymore.”
Rangers had developed a habit of conceding the first goal in matches this season under van Bronckhorst’s predecessor Steven Gerrard and the Dutchman is keen to ensure his players make a more vibrant start to games.
“It is [a message to get across] because you know if you go to these games, away to Livingston can be very hard,” he said.
“They can be physical, they play a lot of long balls. It was important to start well and defend the second ball really good. I think we did it. The only time we got exposed was with the goal they scored.
“Overall, it has been a really good performance from the team. Of course we will always have departments in our game that we can improve but we will do that.”
Van Bronckhorst has had little time on the training ground with his squad since taking charge and there is no respite as a hectic schedule of December fixtures kicks off with a trip to face Hibs at Easter Road on Wednesday.
“Of course (we are learning as we go),” he added. “If you keep playing games like this, last Thursday against Prague and today also was a very confident display we showed. That also gives confidence to the players and now we have two more days to prepare for Hibs on Wednesday. It is another step we can take in our game.”