Djokovic had an 11th-game break in the third set and then survived two break-point opportunities for a 4-6, 6-3, 7-5 victory that gave him a 2-0 record in Group A play. Murray, seeded third, is 1-1 in the round-robin section of the tournament.
Berdych, who has to go against Djokovic in his final group match Friday, won the final five games of a 7-5, 3-6, 6-1 decision over seventh-seeded Jo-Wilfried Tsonga.
Berdych has drawn even with Murray at 1-1 in Group A, leaving Tsonga (0-2) a long shot to earn spot in the semifinals. The top two players in each group advance.
Murray played a very strong first half of the match, using a first-game break to claim the first set as he lost just three points serving in the set. But Djokovic got his first break-point chance in the sixth game of the second set and was able to even the match.
Djokovic took his first lead with a break in the third game of the final set. Murray pulled even with a break, helped by two challenged calls, at 4-4. Two games later Djokovic got his third break of the day. Murray had two break chances in the final game but Djokovic won four straight points and the match.
Berdych had a break in the 11th game of the first set and Tsonga was able to even the match with a break in the fourth game of the second set. However, that was his only break of the match.
Berdych used a break for a 3-1 lead in the third set and, after a hold, seemed to put the match away with a break at love in the sixth game. Five points later the match was over.
Thursday's schedule has second-ranked Roger Federer taking on No. 4-seeded David Ferrer. They are both 1-0 in Group B. The second match has sixth-seeded Juan Martin del Potro playing Janko Tipsarevic, the eighth-seed.
The ATP announced Wednesday the Tour Finals would be contested in London's O2 arena at least through 2015 and Barclays would continue sponsoring the event.
Celebrity Families of 2014 [PHOTOS]