The Springboks dominated possession and territory in the first period but could only manage a 13-5 lead at the break, before three tries in the second period made their fourth successive victory in 2017 a comfortable one.
Wings Raymond Rhule and Courtnall Skosan grabbed their first international tries, with flanker Siya Kolisi and lock Pieter-Steph du Toit also crossing the line.
"The Pumas were a tough team to break down and a lot of credit must go to the leadership of the team, who stayed patient," Coetzee told reporters. "The message at halftime was to stay patient and keep on doing what we were doing.
"We also needed to play in behind them, they were leaving gaps at the back and I think we exploited that. We managed to create the space and the players backed themselves when that happened.
"I am very pleased with the win, although it was not a perfect performance."
The Boks were dominant in the scrums, with tight-head prop Coenie Oosthuizen excelling having come into the side as a replacement for the injured Frans Malherbe.
His showing pleased Coetzee, as did the physicality of the forward pack, who sapped the energy of the visitors.
"We did some good things out there, our scrums were outstanding, with Coenie Oosthuizen delivering an exceptional performance, our mauling has improved and once again the bench made a telling difference when called upon.
"The Argentineans are very physical, but we were spot-on with our defensive tactics. They attacked us close to the rucks and we were ready for that, with the guys putting in some big tackles and double hits."
The Boks travel to Salta for their away match against Argentina next Saturday, and Coetzee knows where his side will need to be more clinical if they are to keep up their winning run.
"We need to improve in a number of areas, such as tactical kicking and our line-outs," he said.
(Reporting By Nick Said; Editing by Christian Radnedge)
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