Djokovic was shutout in the second set but took the first set in a tiebreaker and was able to record a decisive break in the third for a 7-6 (7-3), 0-6, 7-5 win in the second day of Gold Group round-robin play.
Djokovic managed to win just nine points in the second set but had his serve broken just once in the first and third sets.
Tuesday's other match saw Juan Martin del Potro stop Jo-Wilfried Tsonga in a tight 7-6 (7-4), 7-6 (7-5). Tsonga fired 17 aces at del Potro but was hampered by 38 unforced errors. One of those errors was a backhand return into the net that gave del Potro the first set.
The results put Djokovic (2-0) in control of the Gold Group. Davydenko and del Potro, both 1-1, meet Thursday with the group's other semifinal berth at stake. Tsonga (0-2) goes against Djokovic in the other round-robin match Thursday.
Wednesday's Red Group round-robin matches have Andy Murray meeting Gilles Simon, with the winner going to 2-0 in likely locking up a semifinals spot, and Roger Federer playing Andy Roddick, with the loser there likely out of the semifinals running.