Swiss ace Stan Wawrinka also advanced after a grueling battle against Grigor Dimitrov.
Meanwhile, Serena Williams pulled out of her scheduled first-round match as her elder sister Venus Williams advanced.
Here are the key results at Cincinnati Masters.
Federer, Djokovic show no sign of rustiness
It was the first tournament for both Federer and Djokovic after that massive Wimbledon 2019 finale.
Swiss hero Federer beat Argentine Juan Ignacio Londero 6-3, 6-4 to win a rain-interrupted opening match.
Meanwhile, Djokovic overcame Sam Querrey 7-5, 6-1.
Djoker had double-faulted three times as he dropped serve in the opening game.
The win will give both the stars plenty of confidence.
Djokovic glad to get past the challenge
"I ended the match well even if the start was nervy. I'm just pleased with this challenge in quick conditions, I'm glad I overcame it. I'm hoping for better performance in the next round," said world number one Djokovic.
Serena withdraws from the event
The wait for a title since 2018 continued for Serena Williams.
The veteran women's singles star pulling out of her scheduled first-round match against qualifier Zarina Diyas.
This happened just days after she was forced to retire from the WTA Toronto final with back spasms.
Serena has earlier been constantly bothered by a knee injury this year.
My back is still not right: Serena
"I came to Mason [Ohio] on Sunday and have tried everything to be ready to play tonight, and was still hopeful after my practice this morning. But unfortunately, my back is still not right," said Williams.
Venus through, Keys knocks out Muguruza
In women's singles, Venus Williams thrived in a 6-3, 3-6, 7-6 (7/4) victory over Kiki Bertens.
Also, former US Open finalist Madison Keys knocked out 2017 Cincinnati champion Garbine Muguruza 6-7 (4/7), 7-6 (7/5), 6-4.
Angelique Kerber lost in the first round for a second straight week as she fell 7-6 (9/7), 6-2 to Estonian Anett Kontaveit.
Wawrinka battles past Dimitrov, wins for Goffin and Tiafoe
Wawrinka won the first-round battle as he eliminated former champion Dimitrov 5-7, 6-4, 7-6 (7/4).
He will face Russian qualifier Andrey Rublev, a 6-7 (4/7), 6-4, 6-2 winner over 15th seed Nikoloz Basilashvili from Georgia.
Meanwhile, David Goffin beat Taylor Fritz of the United States 6-4, 4-6, 6-4, whereas, Frances Tiafoe beat Gael Monfils 7-6 (9/7), 6-3.