Medvedev silenced the majority of the home supporters at the Qudos Bank Arena with his fourth-straight set victory over Alex de Minaur 6-4, 6-2 over 80 minutes.
The Tokyo Olympic gold medallist defeated Taylor Fritz in straight sets to seal Germany's win over the USA.
Spain, Poland and Argentina continued with their strong form as they defeated their respective opponents 3-0 on Monday for their second consecutive victories in the team event.
After extending his lead to 29-26 in career head-to-heads with Nadal and extending his supremacy over the Spaniard on hardcourts, he combined with Victor Troicki in a 6-3, 6-4 win over Pablo Carreno Busta and Feliciano Lopez
Nadal urged the men's tour and the sport's international governing body to form one major team tournament.
Second-ranked Djokovic leveled the final for Serbia with a 6-2, 7-6 (4) win over top-ranked Nadal on Sunday night, increasing his lead to 29-26 in their career head-to-heads.
World No.1 Rafael Nadal and No.2 Novak Djokovic are set up for a blockbuster finale at the Ken Rosewall Arena for the inaugural ATP Cup, just a week before the year's first Grand Slam - the Australian Open 2020.
Rafael Nadal weathered an early barrage before beating Alex de Minaur 4-6, 7-5, 6-1 to clinch Spain's semifinal win over Australia and secure a spot in the inaugural ATP Cup decider against Serbia.
With the win, the Serbian ended a two-match losing streak against the 23-year-old Russian, who had beaten Djokovic twice in three games in 2019 (Monte-Carlo, Cincinnati).
But after losing to David Goffin 6-4, 7-6 (3) in the singles on Friday, the top-ranked Nadal combined with Pablo Carreno Busta to win the deciding doubles in a match tiebreaker against Belgium.
Djokovic, who has won a record seven Australian Open men's singles titles, was playing in Sydney for the first time in a decade after going 3-0 in singles in the ATP Cup in Brisbane
The top-ranked Nadal didn't drop a set in three group-stage singles matches in Perth in the new international team competition, but was unable to break down a free-swinging Goffin in Sydney.
Novak Djokovic defeated Denis Shapovalov 4-6, 6-1, 7-6 to win the match and take Serbia to the semi-finals.
Hosts Australia became the first team to qualify for the ATP Cup sem-finals on Thursday after some sensational tennis from Nick Kyrgios and Alex de Minaur.
Rafael Nadal and Roberto Bautista Agut sent Spain to the quarterfinals of the ATP Cup.
Medvedev clinched victory against Norway by beating Casper Ruud 6-3, 7-6 (6) in Perth. Karen Khachanov had already routed Victor Durasovic 6-2, 6-1.
Britain No. 1 Dan Evans outclassed Radu Albot 6-2, 6-2 to clinch the fifth-day match after Cameron Norrie beat Alexander Cozbinov by the same score on Tuesday.
The seven-time Australian Open champion won his singles and doubles matches back-to-back to guide Serbia to a comeback win over France on Monday and secure a spot in the ATP Cup quarterfinals.
Spain now has two wins from two starts in Group B and next faces unbeaten Japan to determine first place and automatic qualification for the playoffs in Sydney.
Croatia leads the Group E with two wins from two ahead of Argentina's night match against Austria in Sydney.
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