Wawrinka, who turns 32 on Tuesday, got past Horacio Zeballos of Argentina 6-3, 6-4 in 65 minutes in his opening match of the tournament.
Wawrinka lost just two points on his first serve and recorded seven aces. The Swiss star had only two break points, but converted both of them.
"I'm really happy with the match today," Wawrinka said afterward. "I think it was a great match, especially for first one here for me. It's quite tough conditions, raining and really windy today. It's really windy on the court, so it's never easy. I'm happy with the way I was moving, the way I was playing and my attitude in general was really positive. So it's a great match.
"I'm playing better tennis. I feel that I'm playing good here. I took the confidence from Indian Wells (where he got to the finals). So let's see ... When I'm playing well, when I am confident with my game, I know I can beat anybody."
Wawrinka's next opponent will be Malek Jaziri.
Federer, the 35-year-old Swiss star, has won two of the three tournaments he played this year, winning the Australian Open as well as last week's tournament at Indian Wells, Calif.
He began the Miami Open with a 7-6 (2), 6-3 victory over 19-year-old American qualifier Frances Tiafoe. Tiafoe led 5-4 and 6-5 in the first set, but was unable to get the service break needed to take the set. Federer dominated the tiebreaker, winning the first three points and taking it 7-2.
Tiafoe, who is ranked 101st, could not handle Federer's serve. Federer reeled off 20 consecutive service points in the first set as he improved his 2017 record to 14-1.
"I've hit with Frances maybe twice before," Federer said. "I saw the power he had, the explosivity he had, how he easily can generate pace. He seemed to be fearless, good serving, taking the ball early and making the plays. What I like to see is when a younger player comes out and really feels he has nothing to lose and only has stuff to gain.
"I hope he's going to learn a lot from a match like this just because playing on a centre court with a lot of people, under pressure, saving break points, making break points, playing breakers, that's what it's about. It should feed a player like him with a lot of energy moving forward hopefully.
"I think he's going to be really good."
The biggest upset of the day was sixth-seeded Dominic Thiem of Austria losing 6-1, 7-5 to Borna Coric of Croatia.
Also Saturday, 10th-seeded Tomas Berdych of the Czech Republic saved all three break points against him and beat Andrey Rublev of Russia 6-3, 6-2 in 72 minutes.
Neither player broke serve during that match.
In other matches, eighth-seeded David Goffin of Belgium defeated qualifier Darian King of Barbados 7-5, 6-1; 12th-seeded Nick Kyrgios of Australia beat Damir Dzumhur of Bosnia-Herzegovina 6-4, 6-3; 14th-seeded Roberto Bautista Agut of Spain downed Mikhail Kukushkin of Kazakhstan 6-3, 7-6 (3) and 17th-seeded Ivo Karlovic of Croatia beat Andrey Kuznetsov of Russia 7-6 (4), 6-1.
Diego Schwartzman of Argentina ousted 27th-seeded David Ferrer of Spain 6-2, 6-3; Jaziri of Tunisia outlasted 31st-seeded Feliciano Lopez of Spain 6-3, 4-6, 6-3, and 16th-seeded Alexander Zverev of Germany beat Yen-Hsun Lu of Chinese Taipei 6-0, 6-3.