The Light Blues ran out 2-0 winners over bottom-of-the-table St Johnstone at Ibrox, courtesy of goals in either half from Alfredo Morelos and Ryan Kent.
The victory maintained their four-point lead over Celtic, who beat Ross County 2-1, in the Premiership title race and Van Bronckhorst was delighted his players perseverance was eventually rewarded.
He said: “Defending like St Johnstone did, it will have cost a lot of energy and eventually their energy levels will go down, which will then allows us to attack the spaces more and we did that really well in the second half.
“It was the game we expected - another tough game against a good, well-organised St Johnstone, who are bottom of the league but today, I think they had a really good performance.
“We started really well and created some good chances to go one-up but but we didn’t turn those chances into goals and we didn’t create as much after that.
“It was difficult to find the spaces and scoring just before half-time was very important as it allowed us to be able to play a little bit more the way we wanted to in the second half.
“Finding three players between the lines and getting the passing game we want to stretch our opponent was important. We created some good chances and also scored a good goal from one move.”
Morelos had been criticised for his lack of goals earlier in the season but the Colombian striker notched his fifth in six appearances to the delight of Van Bronckhorst.
The Dutchman added: “I’m happy with his goals recently. He scored a good first goal but also his assist for Ryan. We want our strikers to be in the box at all times, whenever there is danger we want them to be in there.
“I think it was a well deserved goal. We want to continue to keep clean sheets and that’s very important for our game. That is the focus we must have on Saturday against Dundee United now.”
Joe Aribo has earned praise for his standout performances this season and the midfielder picked up another man-of-the-match award.
The Nigerian international insists the main factor behind his impressive form is down to having the ability to play with freedom.
He said: “I’ve just been playing freely and I’m just thankful to god for my talents.
“It wasn’t our best performance at times but it was nice to get over that obstacle and get the three points.
“We spoke about having patience before the game, we know it’s not always going to be a fast start, we have to trust what the boss is saying to us and that’s what we had to do.
“We’re just taking every game as it comes. It’s so important to do that because we can’t look past the next fixture. We need to keep putting in good performances and picking up results.”