Both sides exchanged chances thereafter before City went ahead in the 28th minute.
The goal came through Steven Davies, as he headed home from outside the penalty box.
However, that lead lasted for 10 minutes, as Millwall restored parity in the 38th minute. It was once again a header, this time Darius Henderson finding the target from close range from an Alan Dunne delivery.
The second half was a much more entertaining affair, with both sides expressing their attacking intent.
Davies tried his luck from inside the box for the hosts on 61 minutes, but failed to keep his shot on target.
Four minutes later Cole Skuse's effort from outside the Millwall penalty box went wide, before Malone came close for the visitors with a long-range attempt.
Five minutes later Henry's shot from distance went wide of the right-hand post before Stephen Pearson shot over the visitors' crossbar.