The 20-time major champion was highly economical as he prolonged any rally his opponent tried to dictate and he knew the 15th seed was reeling at having let his second-set lead slip.
After five straight games against him, Schwartzman was desperate to stem the flow as he served to stay in the set.
A magnificent angled backhand volley from Djokovic amped up the pressure and after an hour and 28 minutes he had taken a two-set lead.
Schwartzman had never beaten the world No.1 in six prior encounters but held a 20-7 record on clay this season, including back-to-back finals in Buenos Aires and Rio de Janeiro.
The Argentine bounced back from two sets down to deny Jaume Munar in the second round and then gushed over Paris – the site of his sole Grand Slam semi-final two years ago – following his trouncing of Grigor Dimitrov.
Time was running out if he was to extend his stay in his favourite city.
A break in the sixth game of the third set all but sealed his fate and despite dogged resistance to save match point two games later, the result was complete at the two-hour, 15-minute mark.