Novak Djokovic battled past fifth-ranked Daniil Medvedev 6-1, 5-7, 6-4 to send Serbia into the inaugural ATP Cup final.
Novak Djokovic beat Canada's Denis Shapovalov 4-6, 6-1, 7-6 (7/4) while Dusan Lajovic recorded a 6-4, 6-2 win over Felix Auger-Aliassime.
Novak Djokovic, winner of the last three Grand Slam tournaments, is now over 3,000 points clear of rival Rafael Nadal.
Dominic Thiem will next meet Pablo Andujar of Spain in the ATP 500 clay court event on Thursday.
Yuki Bhambri, ranked 153 to Dusan Lajovic's 61, pushed the Serb all the way but paid the price for inconsistency while blowing a 4-1 lead in the third set.
Yuki Bhambri will face Serbia's No.1 Dusan Lajovic, 61, in the first match of the Davis Cup World Group play-off tie in Bangalore.