Rangers' Josh Windass drew first blood in the Old Firm derby after a mistake by Dedryck Boyata, but his opener was cancelled out by Tom Rogic's curling effort.
The win took the visitors nine points clear of the Gers at the top of the table with a game in hand.
The Ibrox side have slipped nine points adrift of Premiership leaders Celtic, but Murty is determined to finish the season on a high.
"A great victory for us and we deserved it. We have won here a few times now & knew if we could do it whether we'd 11 or 10 men" Brown said.
I thought his performance showed his nerve, his calmness and his agility, particularly when he makes the save and gets up again for the second one when it comes off the post.
'We had to cope with a lot of long balls and direct play.
When we put two strikers on that made it two-versus-two on half a pitch and I'd always fancy Odsonne and Moussa Dembele in that situation against most centre-halves.
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"We go in half-time 2-2, looking forward to the second half, playing with that bit more calmness, and then we end up unfortunately going down to 10 men". I am very proud. "But when he catches him with his elbow, you can see why they give it".
Bain - who signed for Celtic on loan during the January transfer window - was solid throughout the contest, making a handful of impressive stops despite going into the game still awaiting his debut for the Bhoys. "But an absolutely brilliant win and a great day for the supporters".
'He didn't have too much time to think about it.
"People will say I should get it, people will say I shouldn't get it, people will say I will be defined by this one game".
But the Rangers caretaker boss said: "I'm really confident Alfredo will play with confidence".
The Old Firm clash between Rangers and Celtic on Sunday began at a frantic pace, with both teams scoring early on. We squandered a real good opportunity to apply some pressure.