The defending champion passed a tough first-round assignment with a 6-1, 7-6, 6-2 victory over Spaniard Fernando Verdasco (ATP #40).
The defending champion overcame a slow opening to beat German Jan-Lennard Struff 7-6 (1), 6-3 in one hour and 27 minutes.
Nole began his quest for a third US Open title with a 6-3, 5-7, 6-2, 6-1 victory over Jerzy Janowicz at Flushing Meadows on Monday night.
Nole suffered a tough 6-7 (4), 6-7 (2) defeat to Juan Martin del Potro at the Rio Olympics on Sunday evening.
The Serbian duo won their opening round match 6-2, 6-2 against Croatian combination of Marin Cilic and Marin Draganja.
The top seed opened his Wimbledon title defence campaign with a straight-sets victory over British wildcard James Ward.
Nole began his Roland Garros 2016 campaign on Tuesday, defeating world no.95 Yen-Hsun Lu 6-4, 6-1, 6-1.
The 2010 champions will host 2015 title holders Great Britain in the Davis Cup by BNP Paribas World Group quarter-finals on July 15-17.
Andrey Golubev and Aleksandr Nedovyesov defeated Djokovic and Zimonjic 6-3, 7-6 (3), 7-5 to hand the visitors a 2-1 lead.
Nole headlines Serbia’s team nominations and will be joined in the line-up by Viktor Troicki, Filip Krajinovic and Nenad Zimonjic.