The 21-year-old from Thornhill, Ont., defeated the Argentine in just 74 minutes with his 16th ace of the match.
Nalbandian played in the Wimbledon final a decade ago and won the Madrid tournament when it was played indoors back in 2007.
Raonic, ranked No. 23 in the world, will face Swiss ace Roger Federer in Wednesday's second round, having lost to the world No. 3 in the third round at Indian Wells in March.
"I hope I can do much of the same stuff (as I did) in March. I need to serve better than I did then," Raonic said. "I'm playing well and confident and I'm serving well, so that should be a big help."
Raonic says playing a star like Federer is a big challenge, but tennis a simple game once the players step between the lines.
"He's achieved a lot of great things, but when we step out onto the court he's just another tennis player who wants the same thing that I do," Raonic said of Federer. "You respect him, but you don't respect him too much.
"He's set a new level for others to aim for. But on court he's trying to take away from you something that you want."
Raonic ended his win over Nalbandian with 28 winners and just 13 unforced errors in a controlled display of his serving power on clay.
He broke twice from three opportunities while never facing a break point on his own serve.
The hard-serving Raonic started the match with a break and added another in the eighth game of the opening set.
The second set was more one-way traffic for Raonic, with a break of his opponent yielding a 5-4 lead. He completed the win on the first of three match points.
The match marked Raonic's first appearance on the controversial blue clay in Madrid.
Several players, including Raonic, were critical of the surface in the leadup to the tournament but it didn't seem to affect the Canadian on Tuesday.
"I got here early and have been training for almost a week on it. I like the conditions (but) the only tricky thing is the movement," Raonic said. "It's not a natural clay so it bundles up after some time. You get a few bad bounces, but other than that it's not so different.
"It's slippery and hard to change direction, but that benefits me in a way. "