Roger Federer delivered a Centre Court masterclass lasting 89 minutes as the Swiss star hit 48 winners and 16 aces in his 6-4, 6-4, 6-1 victory.
The victory was also Serena's 75th in her last 78 matches, a run that stretches back to her shock first round departure at Roland Garros in 2012
The Russian, who won the French Open on clay last year, brought a 16-match winning streak on the surface into Madrid and was strongly favoured to coast past a player who has been dogged by knee injuries.
Robby Ginepri became the first American to win his way into the second round of the BNP Paribas Open by beating Paoli Lorenzi of Italy 1-6, 6-3, 6-4 on Thursday.
Sara Errani breezed into the semifinals of the Monterrey Open with a 6-1, 6-2 win over Luxembourg's Mandy Minella on Friday.
Fourth-seeded Alexandra Dulgheru of Romania and No. 7-seeded Mathilde Johansson of France were knocked out in the first round of the Monterrery Open on Tuesday.
Alexandra Dulgheru became the latest seed to exit the Barcelona Open when she was beaten 7-5, 6-3 by Spanish qualifier Estrella Cabeza Candela on Wednesday.