The Scottish champions were trailing 2-1 at half-time in the second leg of the Europa League knockout round play-off tie, their aggregate lead over the Bundesliga side cut to a nervy 5-4.
But van Bronckhorst’s decision to replace Borna Barisic with Leon Balogun at the start of the second half, switching to a three-man central defence with John Lundstram dropping back from midfield, saw Rangers regain control as James Tavernier’s second goal of the night smoothed their passage into the last 16.
“It was a purely tactical decision,” said van Bronckhorst. “We trained with three different plans for today and this was Plan C.
“It was difficult, we got a good start, but then we lost two goals. At half-time I had to change the system. It was a system we trained with and talked about and it worked well for us in the second half.
“At home, you don’t want to be defending, you want a good start and we got that. We were unfortunate with the two goals. We could have cleared the ball, there was deflection.
“I knew I had to change things at half-time to get a balance between defending and the transition.
“We needed it. I knew beforehand we had to have the scenarios in place that had to be ready to be executed and the guys did them really well.”
Rangers are in the last 16 of the tournament for a third consecutive season and now eagerly await Friday morning’s draw at UEFA HQ in Nyon
“It’s very important for everyone,” said van Bronckhorst. “I spoke to the players and I told them this is a big moment for the club.
“To be playing Dortmund twice and to get a win away and a draw at home is a very good performance. We're really happy to be going to the next round.
“Wow, the last 16 is only top teams left. We're just really happy to be one of them. Now we'll just wait for tomorrow.”