The Gers keeper saved Jamie McGrath’s spot-kick late on to claim all three points for Danny Röhl’s men after Danilo had fired the Light Blues ahead in the first half.
Midfielder Barron gave away the penalty and he says Butland produced another vital moment when the squad needed him.
Speaking to Rangers TV, he said: “We needed everyone in it together and we showed that tonight.
“Thanks to Jack for saving that penalty and getting us the three points, so we have him to thank for that.
“You need big moments over the course of the season and we had that. We defended as a real team, we were compact and done the basics well and we have come away happy.
“We showed resilience and not every performance is going to be pretty with a lot of fancy stuff. It was good to dig in, it will be like that sometimes this season and we need to keep up that momentum.
“It was a great team performance and it was important to build some momentum and we got the three points and it was a good performance.”
Barron was a standout performer for the Light Blues in the engine room alongside Nico Raskin.
The Scotland international insists he loves nothing better than winning the battle in the middle of the park.
Now he is looking forward to a trip to Hampden to face Celtic in the Premier Sports Cup semi-final.
He added: “It was great and every game I play I like to be in the thick of it, but the most important thing is the win.
“We got a clean sheet and we spoke about that before the game, we want to start games fast.
“I think at times this season we haven’t started quick enough or had one half better than the other. I think tonight we put in a gritty performance.
“The supporters were immense, they are always there for us and it was nice to see them with smiles on their faces.
“We can’t get carried away, we have a big one at the weekend and we want to take care of that one as well.”
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