The significance of the 2-0 win, courtesy of first half goals from Alfredo Morelos and Joe Aribo, was not lost on van Bronckhorst who remains unbeaten after five games in charge of the Ibrox club.
Rangers had to withstand considerable pressure, with goalkeeper Allan McGregor in outstanding form, but saw the match out as Hearts finished it with 10 men after Josh Ginnelly’s 81st minute dismissal.
“We have a big win here,” said the Dutchman. “It’s a difficult place to go. I said that before the game. I think in the first minutes of the game, you could see what Hearts would bring to the game.
“They started really well but I think we defended well with the pressure and the moments where we could be dangerous on the counter attack, we did them perfectly in the first 15 minutes. That gave us a little bit of confidence and the 2-0 was important.
“They also had a lot of chances in the beginning but we kept fighting as a team to get a result here until the end. Especially in the second half when the game got quite physical.
“We were good at keeping the ball, especially when Hearts were with ten men. You knew we could control the game, only one bad pass from Calvin (Bassey) in the back gave them a chance to score. Apart from that, we had control and dominated the last phase of the game.”
Van Bronckhorst was gratified at the game management of his team throughout a hugely demanding 90 minutes.
“For me, that is the most important thing for today and at difficult grounds like this,” he added. “We have to play our own game, keep our standards high. If you don’t have that, it is going to be really difficult. The only outcome of the result really relies on ourselves and today we were there for the whole game and that is why we won the game.”