It took Djokovic's record to 12-1 in opening matches at the ATP Finals, with his only loss coming to David Ferrer on his debut in 2007, and was a return to winning ways after the shock of a 6-2 6-1 defeat by Lorenzo Sonego in Vienna last month.
The Serbian all but admitted after that match that, having ensured he would finish a season ranked number one for a record-equalling sixth time, he considered his job done for that week.
He is looking to match another record by winning a sixth title at this tournament, and is the strong favourite having lost just three matches all season.
The squeaking of Djokovic's shoes was the loudest sound to be heard in an empty arena as the world number one employed his brand of precision tennis.
He looked a little nervous to start with and a poor service game allowed Schwartzman to strike first to lead 2-1, but Djokovic hit straight back and began to pull away as he relaxed into the match.
Another break for 5-3 all but wrapped up the set, and he stamped his authority on the second set with an immediate break.
Schwartzman, at 5ft 7in the smallest man to qualify for the year-end tournament for 40 years, had not beaten Djokovic in five previous meetings and there were no signs at all that was about to change.
The Argentinian's serve was taking a pounding and it took Djokovic just an hour and 18 minutes to wrap up victory.