"I didn't expect this but I think I deserved this", Musetti said in his post-match press conference.
The Rome tournament is a tune-up for the French Open in Roland Garros from September 27.
On the other hand, Wawrinka hasn't played since two Challengers in Prague in August, struggling to find the rhythm in the opener and falling short in set number two to propel the Italian over the top.
As the match wore on, though, and Wawrinka began to put up more of a fight, Musetti continued hitting winners and delicate drop volleys.
Three- times Grand slam champ Stan Wawrinka was comfortably beaten 6-0 7-6 ( 2) by teen Lorenzo Musetti, who won for the very first time on the expert circuit in the preliminary of the Italian Open on Tuesday.
Bulgarian Dimitrov saw off Italian wild card Gianluca Mager 7-5, 6-1, while Croatia's Cilic beat Kazakh Alexander Bublik 6-7 (4-7), 6-2, 6-4.
Ninth seed Rublev, making his debut at the Foro Italico, beat qualifier Facundo Bagnis 6-4 6-4 to book a spot in the second round where he will face Hubert Hurkacz.
World No. 1 Novak Djokovic, a four-time Rome victor, and defending champion and second-ranked Rafael Nadal have first-round byes and begin their campaigns today.
Canadians Milos Raonic and Denis Shapovalov both advanced.
It was a tricky opener for Muguruza against former US Open victor Stephens who also has a pedigree on clay, reaching the final in Roland Garros two years ago. "I think the serve was the key that propelled me through", Lorenzo Musetti said. The 18-year-old qualified for Dubai earlier this year when he was 17, losing against in-form Andrey Rublev in the main draw. "I'm going to enjoy the victory before I start thinking about my match against Nishikori", he said of his upcoming task.
Wawrinka made a string of errors as he lost the first eight games before working his way back into the game.
The two-time Grand Slam champion came from a set and a break down and a 3-0 deficit in the tiebreak to set up a meeting with Estonian 14th seed Anett Kontaveit.
Former French Open victor Kuznetsova had a tougher battle with American Bernarda Pera before pulling through 3-6, 7-6 (7/3), 6-3.