Brands ousted No. 1-seeded Tipsarevic 6-3, 4-6, 6-4 while Dodig, who earlier eliminated second-seeded Marin Cilic, was a 6-4, 6-4 winner over No. 5-seeded Dolgopolov in quarterfinal play.
Dodig had two first-set breaks and converted his only break opportunity of the second set to advance. It was his second straight-set victory this year over Dolgopolov, who is 33 spots higher in the rankings.
Brands' win over Tipsarevic was powered by a nine-ace attack. Brands lost 17 points in 15 games serving and saw just two break points in the match.
No. 3 Tommy Haas ran by sixth-seeded Florian Mayer 6-4, 6-1 in 58 minutes, winning 74 percent of the points on serve. Fourth-seeded Philipp Kohlschreiber stopped Viktor Troicki 6-4, 7-6 (7-3) by converting his only break chance of the match and saving 10 break points from Troicki.
Kohlschreiber goes against Brands in Saturday's semifinals. Kohlschreiber beat Bands 6-4, 6-4 in their only meeting, which came in the BMW Open first round in 2010.
Haas is 1-0 versus Dodig.