Medjedovic, who came through the qualifiers, had stunned Aussie third seed Alex de Minaur in the last 16 and the Serbian came out swinging in the opening set, saving five break points to put one foot in the final.
But Rublev recovered in the second set, improving on his second serve to level the match before dominating the third set on the back of a superb first serve as Medjedovic's unforced error count climbed.
After three semi-final exits this year, former world No.5 Rublev will play his first final since he lost in Hamburg 11 months ago.
"Of course, I would like to (win the title). If it happens, it happens. If it doesn't happen, we keep working, what can I do? Not much to say," he said in an on-court interview.
Fils was also forced to make a comeback as he beat Spanish teenager Rafael Jodar 3-6 6-3 6-2 to register a landmark 100th victory on the ATP Tour.
Jodar, who won the Grand Prix Hassan II title this month, was on an eight-match win streak but he could not stop Fils from reaching his second final of the year. Fils lost to Carlos Alcaraz in the Doha final in February.
Meanwhile Flavio Cobolli produced an upset to beat defending champion Alexander Zverev 6-3 6-3 and secure a place in the final of the BMW Open in Munich.
The 23-year-old Italian made 32 winners and lost just eight points on his first serve against world No.3 Zverev to close out what was a first win over a top-five ranked player.
American No.1 Ben Shelton ended the run of Slovakian qualifier Alex Molcan with a 6-3 6-4 win to reach the final in Munich for the second consecutive year.
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