The top seed will face off on Friday in the quarter-finals against French veteran Arnaud Clement, who defeated Alejandro Falla 6-4, 6-3 earlier on another cloudless day.
"I'm happy that I came through the first round, it was nice to win," said Federer, 2008 champion in his first time at the venue. "Today was a matter of coming through tough situations.
"I played well when I was down 0-40 and serving for the first set.
"This win was not always beautiful but it doesn't matter. I'm sure my best tennis is not far away. I have a bit of a breather now and I'm looking forward to Friday.
Second seed Ivan Ljubicic was meanwhile forced to withdraw from the event with the abdominal strain which forced the Croatian to forfeit a match last week in Rome.
The winner of the Indian Wells title in March will be replaced in the draw by a lucky loser.
In other matches, defending champion Albert Montanes, the Spanish fourth seed, defeated compatriot Daniel Gimeno-Traver 6-1, 6-2. Eighth seed Pablo Cuevas of Uruguay reached the last eight over Marcel Granollers of Spain 7-6 (10-8), 7-6 (7-2).
In ousting Phau, Federer achieved his stated goal of re-starting his clay campaign after an opening loss in Rome a week ago to Ernests Gulbis of Latvia.
The 28-year-old Swiss is bearing down on his career-first title defence later in the month at Roland Garros and next week concludes his tournament tune-ups in Madrid.
"There is always pressure in the first match, it doesn't matter who it's against. The first round in any event is never easy," said Federer.
Phau, 30, and ranked 138, has split his previous two meetings with the 16-time grand slam champion. Federer comes into their match standing 13-4 on the season with his only title the Australian Open over Andy Murray.
"It was my first time on centre court this year, I didn't get a chance to train on it," said the Swiss. "It's a lot bigger than the small practice courts and I had to get used to that.
"Best of three matches can also be over very quickly. I got off to a good start, no hiccups on my serve. Once I won the first set I felt more comfortable, I was able to come up with some nice tennis."
Federer stands atop the ATP rankings as number one for the 281st week and needs just five more weeks at the summit to tie the all-time record of Pete Sampras.
If Federer remains No. 1, he will tie Sampras on June 7 (Halle, Germany, grass-court event) and break the record the following week which proceeds Wimbledon.
In women's play at the Estadio Nacional, Romanian second seed Sorana Cirstea reached the quarters over local teenaged Michelle Larcher de Brito 7-5, 7-5. Fourth seed Anabel Medina Garrigues of Spain ousted Russian Elena Makarova 6-2, 6-3.
China's seventh seed Peng Shuai reached the last eight with a defeat of German Tatjana Malek 6-2, 6-1.