The other semifinal will feature Marin Cilic against 2004 winner Mikhail Youzhny. Cilic advanced to his third semifinal this season after rallying past Andreas Seppi 4-6, 7-6 (8), 6-4, while Youzhny defeated Adrian Mannarino 6-2, 6-3.
"I haven't played Tipsarevic for a long time," said Bogomolov, who beat him in three sets in Tokyo in 2004. "But I do not expect any surprises from him tomorrow."
The Russian-born American, still looking for his first ATP title, broke Lajovic twice in the first set and three times in the second for his second consecutive victory over the 228th-ranked Serb.
Tipsarevic won his second title at the Kremlin Cup on Sunday.
It's the second time this year that Bogomolov has reached a semifinal. He also made the final four in Los Angeles in June.