Keane made eight changes to the starting line-up which has lifted them to second in the npower Championship and was rewarded with goals from Tamas Priskin and Gareth McAuley.
Town had failed to find the net in the opening period of their past nine games, but their double salvo was just enough to see off Millwall despite Steve Morison pulling a goal back on the hour.
"It was a pity we couldn't score in the second half to kill the game off," said Keane. "Credit to Millwall, but I'm glad to be through, there were nothing but plusses.
"It was a very good finish from Tamas and he's putting pressure on the other forwards. We made lots of changes and the last thing we wanted was extra time, but we won the game.
"I could nit-pick but I'd have taken 2-1 before the game. I'm delighted and I'll have a tough job over the next few days."
Source: PA