The 33-year-old Swiss wild card beat the Bosnian, who was seeded sixth, 6-3, 6-4 in one hour and 11 minutes to level their head-to-head record at one all.
Slovakia's Martin Klizan will put his unbeaten record in ATP finals on the line Sunday against top-seeded Dominic Thiem in the St. Petersburg Open in Russian Federation. "I had some tough service games when I was 30-0 down and I always saved myself with some very good serves".
Top seed Thiem, in the hunt for a third title of the year, was pushed all the way by home contender Medvedev but sealed a 6-2 3-6 7-6 (7-2) victory.
The Swiss triple Grand Slam champion, who was a wildcard entry, broke Klizan in the first game of the match and went on to win the opening set in 36 minutes.
"Stan is one of the best players in the world".
Dzumhur squandered two game points in the third game of the second set to lose serve when his forehand found the net, only to create two break points in the following game that could have kept him in the match if he found the way to convert any.
The opponents traded breaks in the deciding set, which ended in a tie-break which Thiem dominated.
Three-time Grand Slam champion Wawrinka, now ranked 88th, seemed on his way for a fourth win over Klizan in as many career matches when he took the opener, but the world No. 65 fought back to seal the victory in two hours and 16 minutes, reports Efe news.
Meanwhile, Kei Nishikori moved a step closer to a first tour-level title since 2016 with a 6-3 4-6 6-4 win over Nikoloz Basilashvili in the quarterfinals of the Moselle Open. "We've played a couple of times in the past and it was always really tough".