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Medvedev remained calm as a robot in the face of fanatic support for Kyrgios to secure a clinical 7-6(1) 6-4 4-6 6-2 win.
The tennis maverick, Kyrgios, returned to the combustible John Cain Arena and gave raucous fans a night to remember.
The artwork was done by Boban Savic, with references to some of Djokovic's greatest accomplishments, including his 37 ATP Masters 1000 titles and 20 major triumphs.
Russia secured their third title and first in 15 years.
US Open champion Daniil Medvedev comfortably beat German Jan-Lennard Struff after Andrey Rublev had demolished Dominik Koepfer in the opening singles.
Medvedev sent the Russian Tennis Federation through by beating Sweden's Mikael Ymer 6-4, 6-4 for an unassailable 2-0 lead in the tie.
Sweden and Novak Djokovic's Serbia took the two best runners-up spots and a place in the last eight by virtue of their better match win-loss records among the second placed sides throughout the group stages.
Zverev, who also beat world No. 1 Novak Djokovic on Saturday, becomes only the fourth player to beat the top two players in the world in the semis and final of the season-ending tournament.
Defending champion Medvedev stormed into the final after crushing Norway's Casper Ruud 6-4, 6-2.
Djokovic avenged his US Open final defeat with a 4-6, 6-3, 6-3 victory.