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The world No. 1 took one hour and 32 minutes to defeat the rising Greek star.
The Serbian will meet either five-time Madrid champion Rafael Nadal, the world number two, or Stefanos Tsitsipas in Sunday's final.
Rafael Nadal beat Stan Wawrinka 6-1, 6-2 to set up a clash with Stefanos Tsitsipas, who edged Alexander Zverev 7-5, 3-6, 6-2 in the other semi.
Murray, a three-time Grand Slam champion, has not played competitively since his first round exit at the Australian Open in January. He has since undergone hip resurfacing surgery.
The 20-times Grand Slam champion became the second man in the Open Era to claim 100 titles after American Jimmy Connors who won 109.
The Spanish second seed tamed the Tsitsipas serve and racked up 28 sparkling winners against the man who had knocked out double defending champion Roger Federer in the fourth round.
Top seed and six-time champion Djokovic will meet Frenchman Lucas Pouille, a maiden Grand Slam semifinalist, on Friday for a place in Sunday's final.
The 17-time Grand Slam champion broke Tiafoe's first service game in each set and with a second break in the third set wrapped up the victory in an hour and 47 minutes.
With a victory that triggered a chorus of singing from Greek fans in the terraces, Tsitsipas became the youngest semi-finalist at Melbourne Park since American Andy Roddick, also 20, at the 2003 tournament.
The night after Roger Federer was stunned by Greek tyro Stefanos Tsitsipas, there was another sniff of an upset at Rod Laver Arena as 22-year-old Medvedev rocked the Serb with a furious assault of power hitting.