Medvedev claimed the biggest win of his career by defeating world No.1 Novak Djokovic in the last eight but crumbled against another Serbian as Lajovic rallied from 5-1 down in the opener to make it 10 sets in succession.
By reaching his first ATP Tour final, where he will face Fabio Fognini, unseeded 28-year-old Lajovic guaranteed he will crack the top 25 of the rankings for the first time.
Medvedev looked to be cruising as he moved to within one game of the opening set with a second break of serve, but Lajovic managed to stage a phenomenal comeback.
There was no let up from the Serbian in the second set and Medvedev only held at the third time of asking.
The Russian never looked like replicating his opponent's feat and forcing a decider, though, with a wayward backhand ensuring Lajovic's sensational run will continue through to the showpiece.