Federer has been plagued by injury problems this year and the world number three lacked rhythm and confidence in his opening match at this year's grass-court Grand Slam.
The 34-year-old, without a major title since 2012, will play British qualifier Marcus Willis for a place in the last 32.
"I was telling myself how nice it was to be back at Centre Court. I've worked so hard since February to be ready for Wimbledon," Federer said.
"We'll see if I'm fully fit as I go further in the tournament, nobody knows, not even me."
Federer's 303rd Grand Slam singles victory moved him within three of Martina Navratilova's record and gave him 302 more wins than world number 706 Willis has managed.
Willis, 25-year-old tennis coach, defeated Ricardas Berankis, ranked 652 places above him, to win his first ever Grand Slam match and Federer is as fascinated by his fairytale rise as the rest of the tennis world.
"I was very intrigued about his story. It's exactly what this sport needs when guys come from nowhere," Federer said.
Bidding to win Wimbledon for a record eighth time, Federer would become the oldest man to triumph at the All England Club in the Open era and the oldest Grand Slam champion since Ken Rosewall in 1972 if he lifts the trophy in two weeks time.
Even in the twilight of his career, Federer's pedigree is head and shoulders above most opponents not named Novak Djokovic, but the contrast was especially striking against world number 52 Pella.
Yet missing the recent French Open due to a back injury -- ending his record run of 65 consecutive appearances in Grand Slams -- prolonged a frustrating year for Federer, who also had surgery on a knee injury following January's Australian Open semi-final loss to Djokovic.
Federer arrived at Wimbledon on the back of his first defeat to a teenager in 10 years against Germany's Alexander Zverev in Halle.
It was the same story in the second set, with Federer well short of his best but eventually edging another tie-break before finally making his class count in the third set.
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