KEY BISCAYNE, Fla. — Roger Federer kept waving in apology, twice after he dribbled winners off the net cord and once when he slammed a volley that nearly knocked his opponent down.

Afterward Federer praised 19-year-old American qualifier Frances Tiafoe, who acquitted himself well before a near-capacity stadium crowd at the Miami Open. But there are limits to Federer's politeness, and he beat Tiafoe 7-6 (2), 6-3 Saturday.

Returning to the tournament after a two-year absence, Federer took the lead with a flawless tiebreaker and gradually pulled away from Tiafoe.

"I think he's going to be really good," Federer said. "He's got big shots, and I like his mindset. That goes a long way."

The 35-year-old Federer wins raves these days for his recent resurgence, and he is hoping it extends to his first title at Key Biscayne in 11 years. Tiafoe, 19, is touted for his potential to improve the bleak American tennis landscape.

Facing a top-10 player for the first time, Tiafoe forced Federer to play well to win.

"He stayed with me for a very long time," Federer said. "That can make you nervous if I wouldn't have been so confident. So I thought it was an enjoyable match. I thought we both played very well, and both can maybe walk away from this match quite happy, which is not often the case in tennis."

Tiafoe smiled when he told of Federer's assessment.

"One is more happy than the other," he said with a smile. "Nah, I'm definitely happy. We both played pretty well. It was good tennis."

Tiafoe, a Maryland native ranked 101st, did almost nothing wrong in the first set. He committed just one unforced error in the tiebreaker, netting a backhand to end the longest rally of the match, but Federer took advantage of the small opening.

"He was rock solid," Tiafoe said. "He didn't give me anything."

Federer is 14-1 in 2017, including his 18th Grand Slam championship at the Australian Open and a title at Indian Wells last week. His potential path at Key Biscayne is made easier by the absences of six-time champion Novak Djokovic and two-time champion Andy Murray, both sidelined by elbow injuries.

Perhaps the biggest obstacle will be fellow Swiss Stan Wawrinka, seeded No. 1 in an ATP Masters 1000 tournament for the first time. Wawrinka dominated with his serve to win his opening match against Horacio Zeballos, 6-3, 6-4.

Americans John Isner and Sam Querrey won in straight sets, as did 19-year-old German Alexander Zverev.

In women's play, No. 6-seeded Garbine Muguruza rallied past No. 30 Zhang Shuai 4-6, 6-2, 6-2. American Bethanie Mattek-Sands eliminated No. 17 Anastasia Pavlyuchenkova 4-6, 6-0, 6-3.

Federer's only wobble came when he was broken in the opening game of the second set. He lost just seven points in his 10 other service games and whacked a service winner on match point, then met Tiafoe at the net for a warm exchange.

"It was an honour playing you," Tiafoe said. "I hope we can play again, hopefully not so early in the tournament."

Federer smiled politely.