Curtis Woodhouse did his job on the post to clear a Carl Asaba header from a 12th minute Millwall corner.
Veteren midfielder Don Hutchison was unlucky not to score, flashing a well executed volley just wide.
Nick Barmby had the best of a series of half-chances for City, lobbing just over.
The last action of the half was a mix-up between Boaz Myhill and Damien Delaney that gave Asaba a chance to snatch at a shot from just outside the box that went wide.
Ben Burgess came on at half time as Peter Taylor changed to a formation talked about before the game.
Despite City's new attacking style, it was Millwall who scored first. A cross came in and Myhill saved from Dunne, but the rebound fell to Asaba who shot into the empty net, just after the hour mark.
This prompted Taylor to use his substitutes again, bringing on Ryan France and Craig Fagan.
City were showing spirit to fight their way back into the game being played under heavy rain, but were failing to create anything to worry the visitors.
That was until a nice move 9 minutes from time that gave City the equaliser. Curtis Woodhouse played a good ball out wide to Andy Dawson in space. He crossed from deep and Burgess did well to loop a header past Andy Marshall and make it 1-1.
The Tigers then went after a winner, but it was the Lions who almost stole it. Jermaine Wright was found totally free and onside in the box, but his shot was fired at Myhill.
City continued to go after it until the final whistle, but a winner didn't come and both sides will be happy enough with a point.
City line-up (4-4-2): Boaz Myhill; Mark Lynch (Ryan France, 65 mins), Leon Cort, Damien Delaney, Andy Dawson; Stuart Green, John Welsh, Curtis Woodhouse, Stuart Elliott (Ben Burgess, half time); Chris Brown (Craig Fagan, 65 mins), Nick Barmby.
Un-used subs: Matt Duke, Marc Joseph.