The fourth-ranked Muguruza had eight aces and didn't concede a single break point to Vinci in the World Group playoff tie on outdoor red clay. She broke Vinci's serve four times at the Lleida Tennis Club in northeastern Spain.
The result keeps Spain in the World Group, following a 4-1 defeat to France in February. Spain had beaten Italy the last time the two teams had met, in 2008.
''I don't think any of us thought we were going to win 3-0 against Italy,'' Muguruza said. ''Our goal was to get back in the World Group. Now we have a different goal and hopefully one day we can win the Fed Cup.''
Muguruza had beaten Francesca Schiavone in two sets on the first day of singles, when Carla Suarez Navarro eased past Vinci 6-1, 6-1.
Schiavone was a last-minute substitute after Sara Errani strained a muscle in her right leg.
''It was a tough weekend,'' Vinci said. ''I played not so good but Garbine played an incredible match today. She was so aggressive it was tough to try and move her around. She played much better than me.''
The Wimbledon runner-up, Muguruza now has a 6-0 record in the Fed Cup, with victories against former No. 1-ranked Jelena Jankovic and former French Open finalist Simona Halep.