The contest started brightly with Carlisle showing early attacking initiative.
Inside the first five minutes the Cumbrians could have easily found themselves two goals ahead but for some very smart work between the sticks from Lenny Pidgeley.
In the fourth minute, Bolton loanee Johann Smith slipped past Tony Craig with confident ease down the right flank but, with numbers in the box, Lions captain Paul Robinson did exceptionally well to read the situation and clear the danger.
From the resulting corner, Chris Lumsdon sent his 25-yard volley crashing into the bottom right corner only to see Pidgeley produce an excellent save.
The Cumbrians continued to pile on the pressure but were denied again a minute later by more excellent work from the home keeper.
Zigor Aranalde's cross from the left found Danny Livesey, who fired a shot on the turn from eight yards which Pidgeley somehow deflected wide.
However, this was as good as it got in the first half as both sides struggled to find any rhythm or cutting edge.
Both showed a lot more confidence going forward in the second half and Millwall took the lead on 52 minutes with their first real chance.
Craig crossed from the left to Harris who cut inside Livesey and then left Anthony Williams on the floor with his second touch before firing home from five yards.
Seconds later, Harris provided another moment of sheer class when, with his back to goal, he chested the ball down and fired a dipping volley on the turn. Williams was well beaten but the ball bounced inches wide of the right-hand post.
Carlisle fought back well and should have equalised on 67 minutes. Smith was given ample time and space ten yards from goal by a selfless pass from Luke Joyce but Pidgeley saved low to his left.
But on 81 minutes, Harris ended the contest when he reacted quickest to a Craig shot which bounced back off the bar.