In the 20th minute, Franck Ribery shot straight at Gikiewicz from 10 yards.
Robert Lewandowski launched the ball over the bar with five minutes of the first half left.
Braunschweig had seemingly kept Bayern Munich at bay in the first half, but David Alaba had other ideas. After Robben won a free kick on the right, Alaba directed the ball into the net off the underside of the crossbar at the stroke of half time.
Mario Gotze doubled the lead in the 56th minute as he broke free of two Braunschweig defenders and rolled the ball past Gikiewicz for a simple finish.
Alaba could have scored his second goal of the night in the 72nd minute, but shot straight at Gikiewicz from inside the penalty area.
Bayern Munich are aiming to become the first club to win the DFB-Pokal for the third year in a row.