The Light Blues could have cut the gap at the top to three points but instead goals from Tom Rogic, Moussa Dembele and sub Odsonne Edouard saw the Hoops win 3-2 and stretch their lead at the top to nine points with a game in hand.
Brown had heard how Graeme Murty had said his Rangers players had celebrated when they got the Hoops in the Scottish Cup semi-final and fancied their chances coming into Sunday’s league clash.
The skipper said: “They talked all week and we just sat down. We did our talking on the park. We always do our talking on the park. Whether we win or we lose, we always fight till the last minute. That’s happened a few times to us now.
“Whether there is 11 of us or 10, we have always got that belief. We are definitely on a high. We always believe that we can come here and get the three points and we did that today.”
Brendan Rodgers, undefeated in Old Firm clashes, also reckoned it was as satisfying a win as he has had against Rangers.
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He watched his team battle back from going down twice and then to win the game with 10 men, after Jozo Simunovic’s red card.
Rodgers said: “It was like a game I’d watch when I was growing up watching Celtic v Rangers. We made a mistake to go behind.
“In fact, we were behind twice but we had great pride in the team. We played well and showed that toughness and character you need.
“In fairness to Rangers they have been in really good form and this was at the height of their confidence levels. For us to go on and win it and win it with 10 men was a splendid performance.”
Rodgers wasn’t surprised match-winner Odsonne Edouard came up with his moment of magic.
He said: “I have said all along he is a big talent. He is one of the best young players I have worked with.
“He has everything – touch, movement, speed, work ethic and a natural in-built football brain. I am delighted for him and for the team.”