After making the third round of the Indian Wells Masters event Federer told Swiss reporters that he had tried to speak to Djokovic - head of the Player Council - ahead of the meeting where he oversaw the narrow passing of a vote not to renew Kermode's contract.
"It's a very special win today".
However, Wawrinka did play a key part in one of the most extraordinary rallies of the match.
"Today, with Novak being number one, top-seeded here, it's a very incredible win for me".
"What an effort as Roger just being Roger gets it done", one commentator enthused.
Nadal started impressively with a hold to love and Schwartzman also hit the ground running in a tight opening set, as break points proved to be elusive.
Djokovic displayed his frustration by banging his racquet against his foot until it crumpled, but it did nothing to improve his fortunes as Kohlschreiber opened the second set with a break.
When Wawrinka sent a backhand long, Federer broke again to take a 2-1 lead in the second set.
Then it was Kohlschreiber's turn to show some nerves as a string of four errors, including a double fault gave Djokovic a break back. Because he was serving better, he started to swing more freely and then it was tough, Federer said.
Elsewhere, 40-year-old Ivo Karlovic took down Indian No. 1 Prajnesh Gunneswaren 6-3, 7-6 (3). Nadal is 6-0 against the Argentine. Both Federer and Nadal used their voice to insist that if there is to be a change, players must be consulted with, something that they say wasn't done. "So it's a positive victory for me".
The 17-time Grand Slam champion, who owns three Indian Wells titles, needed just 72 minutes to get past world number 192 Donaldson, who returned to the tour in February after six months sidelined by a knee injury.
Federer has dominated the rivalry with his friend and countryman 21-3, with all three of Wawrinka's victories coming on clay courts.
Each arrived at this latest encounter in good form: Federer won in Dubai, Wawrinka made the final in Rotterdam, and produced consistent and powerful tennis through three-set wins over Dan Evans and No29 seed Marton Fucsovics.
Poland's 67th-ranked Hubert Herkacz upset sixth-seeded Kei Nishikori of Japan 4-6, 6-4, 6-3 to reach the last 16 of a Masters 1000 event for the first time.
The 22-year-old will next face Canadian teenager Denis Shapovalov, who continued his run of dominant serving without being broken on his way to an impressive 6-4 6-2 win over 10th seeded Croat Marin Cilic.
Eighth-seeded American John Isner made it safely through, downing Argentina's Guido Pella 6-3, 6-4 to set up a meeting with Russia's Karen Ahachanov, a 7-5, 6-3 victor over Russian lucky loser Andrey Rublev.