Millwall seized the initiative in first-half injury time when Harris stroked home a penalty after being felled in the box by Chris McCready.
Brkovic, the Croatian midfielder on loan from Luton, then marked his return from a hamstring injury with a well-taken 53rd-minute goal to compound Crewe's dismal recent run.
Dario Gradi's men have now taken just two points from their last seven league games, but will count themselves unlucky to have fallen behind to Harris' first goal of the season after fashioning the pick of the first-half chances.
Simon Church and Byron Moore both squandered early chances before McCready rattled the woodwork with a close-range header on 24 minutes.
Struggling to make the most of slightly superior possession, Millwall then suffered a blow with the interval beckoning when Gary Alexander, the hat-trick hero of the Boxing Day win over Brighton, was forced off with a broken nose.
Millwall's most promising move up to that point had come when a dipping Bryan Hodge effort forced the Crewe goalkeeper, Ben Williams, to claw the ball away from beneath the crossbar.
As the half entered its dying seconds, McCready needlessly brought down Harris, who gleefully stepped up to the spot to open his account for the season.
Immediately after the restart Harris almost picked up from where he had left off, sending a curling effort agonisingly wide of Williams' far post.
Millwall did not have to wait long for a second goal, the returning Brkovic latching on to a cleverly-worked Dave Brammer free-kick to ensure that Jackett's side ended 2007 on a positive note.