Nadal needs to reach the final of the $2,315,250 tournament to take back the top ranking from Djokovic, who has finished the last two years as world number one.
The Spaniard has won 10 titles this year, including the French and U.S. Opens, after coming back from his latest spell on the sidelines to allow his troubled knees time to recover. He is now aiming to extend that brilliant run in Asia.
The 27-year-old traded breaks with Kohlschreiber early in the opening set on Wednesday before securing another in the 10th game when the German hit a forehand long.
The second set went with serve until a tiebreak where Nadal's serve helped him prevail 7-3 to rack up his 19th consecutive win since losing in the first round of Wimbledon to Belgian Steve Darcis.
"Today the serve, in my opinion, helped in the important moments," Nadal was quoted as saying by the ATP Tour.
"But it's true that his level of tennis I think was just brilliant tonight. I won because I played a great match. If not, I would not be here with a victory."
Fognini booked his last eight spot with a 6-0 6-2 thrashing of former world number one Lleyton Hewitt.
Big serving American John Isner was another second round winner as he prevailed 6-2 6-7(3) 6-4 over Spanish qualifier Roberto Bautista. He will next play Czech world number five Tomas Berdych who claimed a walkover over Russia's Nikolay Davydenko.
Djokovic is back on court on Thursday when he takes on Nadal's compatriot Fernando Verdasco in second round action.
(Writing by Patrick Johnston in Singapore, Pritha Sarkar)
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