Millwall had the better of the chances in the opening period, but their finishing let them down in front of goal.
The combination of the young fresh legs of on-loan striker Will Hoskins and the experienced head of Neil Harris worked well in all areas of the pitch, except the 18-yard box.
Millwall had the first chance of the game inside the first minute when Harris broke down the right-hand side and crossed the ball to Brkovic, but his shot was tipped around the post by Cherries keeper Gareth Stewart.
Hoskins then got into the game and picked up the ball on the halfway line and beat three defenders before blasting his shot high and wide.
The best chance of the first period came on the half-hour mark when a long clearance by Lions defender Zak Whitbread forced Stewart to come out of his area.
He mis-timed his clearance but, with the goal gaping, Harris failed to keep his shot from 25 yards on target.
Brkovic then went close but his shot fizzed across the goal-line with no one nearby to put the finishing touch.
Five minutes after the break the home side finally made the breakthrough. Harris played in a deep cross from the right to find an unmarked Brkovic who headed home from close range.
Millwall secured their place in the hat for the third round draw minutes later when Brkovic played the ball through to the impressive Hoskins who beat the offside trap and slotted a shot past Stewart.
Bournemouth did manage to pull a goal back in the 74th minute when Lenny Pidgeley parried Jo Kaffour's shot into the path of Shaun Cooper who fired home from close range.
However, it was too little, too late for the visitors.