The win kept the eighth-seeded Argentine on course for a place in the season-ending Masters Cup and a 10th career title.
Nalbandian is one of four players chasing the final two spots for the prestigious tournament in Shanghai. James Blake and Jo-Wilfried Tsonga, who played their semifinal match later Saturday, are also in contention.
Juan Martin del Potro, beaten by Nalbandian earlier in the tournament, is the other player hoping to qualify.
Davydenko's strong resistance finally cracked in the seventh game of the deciding set when the Russian lost his serve and Nalbandian held his easily for a 5-3 lead.
Nalbandian won on his second match point when Davydenko's return sailed long.
The sixth-seeded Davydenko lost the first set in 28 minutes, winning just four points on Nalbandian's serve as the Argentine won 79 percent of points on his first serve. Davydenko made 13 unforced errors, mostly from the back of the court.
The Russian picked up his game in the second set, improving his serve and pinning Nalbandian to the baseline with accurate forehands.
Nalbandian found himself under pressure on serve at 6-5 down in the 12th game. He double-faulted and lost the second set when he hit the ball into the net after Davydenko had returned his weak second serve.
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