The Serb, who beat Roger Federer in the Basel final on Sunday, came back from 2-0 down in the first set and secured the decisive break of serve when Monaco whipped a forehand into the tramlines at 15-40 and 3-4 down.
Monaco forged ahead to lead 5-2 in the second set but after seeing off a set point, Djokovic roared back to set up a meeting with either German 16th seed Tommy Haas or Arnaud Clement of France in the next round.
Swedish ninth seed Robin Soderling kept alive his hopes of snatching a place at the ATP World Tour Finals in London by defeating Croatia's Ivo Karlovic 6-4, 7-6 (8/6).
Soderling is one place outside the eight qualifying berths for the year-end event but needs to at least reach the final here to stand any chance of securing one of the last two available spots and will meet Russian Nikolay Davydenko, currently seventh in the race to London, in the next round.
Russian former world number one Marat Safin, who is playing in his last tournament before retirement, faces US Open champion Juan Martin Del Potro later, with top seeds Federer and Rafael Nadal also in action.
Federer meets France's Julien Benneteau and Nadal takes on fellow Spaniard Nicolas Almagro, with fourth seed Andy Murray of Britain beginning his campaign against America's James Blake.
The 2.75 million-euro event is the final Masters tournament of the year and boasts a line-up that features every top 15 player except the injured Andy Roddick.
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