Djokovic has been well received on his return to Australia following his deportation on the eve of the Grand Slam last year for not being vaccinated against COVID-19 and the 35-year-old delighted fans by comfortably going up a set and a break.
Canada's world number 18 Shapovalov raised his game to draw level at 3-3 in the second set but surrendered his serve after a wayward shot and a double fault as Djokovic surged ahead 5-4 before closing out the quarter-final clash on serve.
Top seed Djokovic has won his previous three meetings with Medvedev, who last beat him in the 2021 U.S. Open final.
"It'll be another long night. There's not going to be too many short points unless we both serve well," said Djokovic, who is 8-4 overall against the Russian.
"Against him, you have to be ready to go the distance physically and mentally... game-wise, he's one of the best in the last five years. He's established himself ... and he's someone I respect a lot.
"We've had some amazing battles over the years and hopefully we can have one more."
See all the details from the match
Third seed Medvedev earlier advanced with a 6-3 6-3 win over compatriot Karen Khachanov in their first tour meeting since 2019 to improve his record against him to 3-1.
"I'm happy that I managed to raise my level, especially in the end of both sets and I'm really happy to be in the semis," Medvedev said.
Japan's Yoshihito Nishioka knocked out the last remaining Australian in the ATP 250 event as he beat qualifier Alexei Popyrin 7-6(4) 6-7(8) 6-2 to set up a semi-final clash with Sebastian Korda, seeking a first win over the American.
Korda faced sixth seed Jannik Sinner after straight-sets wins over Andy Murray and Roberto Bautista Agut and the world number 33 was unstoppable again in his 7-5 6-1 victory over the Italian who struggled with a hip issue.
"It was a great match until something started to bother him," Korda said. "So I just wish him all the best for the coming weeks and the Australian Open coming up."
