WATCH the ATP Tour LIVE on beIN SPORTS | via Foxtel, Kayo Sports, Fetch TV and beIN SPORTS CONNECT
Djokovic made a fast start by breaking in Medvedev's second service game, but there was concern when the 21-time grand slam winner required a lengthy medical timeout at 5-2 up in the opening set.
With Djokovic's long-awaited return to the Australian Open just over a week away, the sight of the Serbian clutching his left hamstring was an unwelcome one, but he eventually returned to the court to take the opener 6-3.
Having shown his staying power in a low-key start to the second set, Djokovic claimed the vital break following some excellent work at the net in the seventh game, though Medvedev was ultimately the master of his own downfall after producing a double fault at break point.
Djokovic then faced break point in the next game as Medvedev desperately tried to claw his way back into the contest, but a huge second serve eventually saw him hold off the Russian, who was unable to trouble him thereafter.
Speaking court-side after teeing up his 131st ATP Tour final, Djokovic played down concerns over his hamstring issue, saying: "Thankfully, it was nothing too serious.
"If it was, I wouldn't have been able to continue. I just tried with a medical timeout and some anti-inflammatories and I just settled in.
"The more the match went on, the more my hamstring was warmer, I guess, and bothering me less. So hopefully tomorrow it will be OK."
Asked whether he considered retiring in order to save himself for the first grand slam of the year, Djokovic added: "I can't say it didn't cross my mind today on the court.
"But you just can't calculate on the court. At this stage of my career, every match counts, every match is a present in a way, so I just try to give my best and win wherever I am."
Yoshihito Nishioka also struggled with an injury in the day's other semi-final, but the world No.36 was less fortunate than Djokovic as he retired midway through his clash with Korda.
Korda took a close opening set via a tie-break after Nishioka ranted at a second umpire in as many days, raging when a point was replayed after an error from a line judge.
Nishioka saw his serve broken in the first game of the second set before calling a medical timeout after seeming to struggle with a leg injury, and his subsequent retirement ensured Korda advanced to his fifth ATP Tour final.