A first-half mistake allowed Thomas Muller in to find Mario Gotze at the far post and he tapped home for his third goal in two games.
David Alaba had a big hand in the second, forcing Halfar to turn the ball into his own net under pressure in the 66th minute, compounding a difficult match for the midfielder.
The result leaves Pep Guardiola's men top of the Bundesliga, having extend their unbeaten start to the season to six games.
And Cologne's defence, which conceded their first goal of the season at Hannover in midweek, was eventually undone after 19 minutes.
Halfar's error allowed Robben to play in Muller, whose drilled ball across the goal eventually found Gotze at the far post, enabling the German to tap home with a simple finish.
Muller nearly added a second four minutes later, forcing a great save from Timo Horn following Robert Lewandowski's lay-off, before Robben tested the keeper again with curling effort in the 33rd minute.
The visitors' inability to find a second was nearly punished 10 minutes before the break, with Neuer on hand to deny Adam Matuszczyk and Anthony Ujah in quick succession.
Having allowed Bayern to take the lead through his first-half error, Halfer's misery was complete when he turned the ball into his own net.
Some good work from Robben allowed Lewandowski to break free in the box, setting up Alaba, who was then tackled by Halfar, before the ball trickled into the net.
Substitute Xabi Alonso almost capped off the triumph 19 minutes from time, but the Spaniard was denied his first goal for the club as his 30-yard effort was saved by Horn.
