Hibernian came within 10 minutes of ending Celtic's 57-match unbeaten run in Scottish competition as a double from John McGinn had them 2-1 ahead.
But Callum McGregor levelled up on 80 minutes for his second of the game to rescue Brendan Rodgers's side - and the team's record in the process.
Despite those two players both bagging a brace, the veteran Celtic goalkeeper also emerged with a great deal of credit after pulling off what Brown claims was an "incredible" save to deny the former Rangers defender from point-blank range.
And Brown told the Hoops' official website that the Rangers legend asked him afterwards how he managed to keep it out.
He said: "I spoke to Steven Whittaker after the game and he said to me, ‘how did he save it?!”
“At the time, you think, ‘what a save’, but when you see it back, it’s incredible, frightening. The way he has got there so quickly shows it’s not about his age, it’s about how much he wants it and what he does day in, day out in training.
"He is probably as fit as he ever has been and he is 34 years old."