Federer, who won the Australian Open in January, produced a confident display to win 6-2, 6-1 at the Indian Wells Tennis Garden.

"I thought the match went really well," said Federer.

"It was a rocky start in the beginning, just finding the groove, finding the rhythm, seeing the ball.

"I'm very pleased how it went.

"Moving on to the next round, it's going to be different."

Rafael Nadal, who lost to Federer in the final of the Australian Open, was also a comfortable winner today.

The Spaniard surged into round three with a 6-3, 6-2 win over Argentina's Guido Pella.

World number two Novak Djokovic also claimed a straight sets win but his was far from comfortable against Great Britain's Kyle Edmund as the Serbian won 6-4, 7-6.

Kei Nishikori of Japan cruised into the next round of the tournament with a 6-3, 6-4 win over Dan Evans of Great Britain.

In the women's singles event, Garbine Muguruza of Spain moved into the next round after coming from behind to defeat Kayla Day of the United States. 

Roared on by the home crowd, Day took the opening set 3-6.

However, Muguruza, who won last year's French Open title, turned the match around by taking the second and third sets 7-5 and 6-2 respectively to advance.

Third seed Karolína Plíšková of the Czech Republic was knocked out of the tournament today after she was beaten by Dominika Cibulkova of Slovakia.

Plíšková started well and took the first set 6-2 before her opponent came from behind to win the next two sets 7-6, 7-6 to secure her place in the next round.

Great Britain's Johanna Konta was also eliminated after going taking the lead in her match against France's Caroline Garcia.

Konta took the opening set 2-6 but Garcia took the second 6-3 to level the match.

It was Garcia who ultimately prevailed, winning the decisive third set 7-6.