The German, who is based in the Principality, reached the third round as he tamed the 18-year-old who broke through for a Miami semi-final last month.
Rafael Nadal starts his bid for a 12th title here later, with an opening match in the second round against fellow Spaniard Roberto Bautista Agut.
The 21-year-old Zverev played the semi-finals in Monte Carlo a year ago but has yet to hit his stride this season.
That may be starting to change.
“This is the first time this season I’ve felt really healthy,” said Zverev, who lost prematurely at both Indian Wells and Miami, as well as in Marrakech last week.
“I’ve been training well but haven’t been able to take that into matches.
“I live just 500 metres from here, I’m comfortable on this court. I’m starting to feel better about my game.
“I’m really ready for the clay season.”
Canadian Auger-Aliassime has made a fast rise in the rankings from 175 a year ago to his current 33rd.
Zverev swept the opening set in 30 minutes but had to get through a series of three straight breaks of serve between him and his opponent before finally advancing in 78 minutes.
The third seed broke six times and will next face Italy’s Fabio Fognini, who reached the third round when French opponent Gilles Simon was unable to play their match due to back problems.
Greek sixth seed Stefanos Tsitsipas moved ahead, defeating Mikhail Kukushkin 6-3, 7-5.
“I need to maintain my focus, my concentration, my aggressive mindset when I’m on the court,” Tsitsipas said.
“If all these are combined, then I have nothing to fear and I have nothing to be afraid of when I’m on the court.
“This is the first big clay court tournament, not everyone is very well prepared for that. It’s been a long hardcourt court season before the clay.”
Britain’s Cameron Norrie defeated Marton Fucsovics of Hungary 7-6 (7/3), 6-3, while Pierre-Hugues Herbert stunned 2018 finalist and fifth seed Kei Nishikori 7-5, 6-4.
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