However, he finally got his break to take a decisive 5-4 lead and went on to take the set 6-4 to level the match.

The decider was another closely run affair, with Djokovic doing just enough to take it 7-5 and win the match.

“I wasn't feeling that great on the court. Physically wise, I was a bit slow. I kind of couldn't get into a great rhythm. With reactions, as well. But I'm just happy to win the first match. I knew that it was going to be a long one,” Novak Djokovic told the tournament’s official website.

Djokovic, who also defeated Davydenko in the final of the last year’s ATP finals in Shanghai, gave credit to his rival.

“Davydenko is in great form, [a] very aggressive player. But in the end, [I am] quite happy to get through. I really think he was a better player in the first two sets and maybe overall in the whole match. But when you have bad days, you still manage find a way to win. I think that's something that is great to have in your game,” he added.

Two more singles matches are scheduled for Tuesday in the English capital. In Group A, home favorite Andy Murray will try to upset World No. 1 Roger Federer.

In another game, Juan Martin del Potro takes on Fernando Verdasco.