Federer lost the first set in the tiebreak, but fought to win the second set by 7-5 and force a tiebreak.
And in front of his fans, Federer kept his cool and composure to beat Kyrgios 6-7 (5) 7-5 10-7.
At 5-4 of the second set, with Federer preparing to serve in the match, Nadal approached him and said: “After five strokes (in the rally), you are earning more (points) than him.
“Like 8-5 for you – I checked the numbers so the percentages are much better for you.
"I know it's hard because he reads the ball so well. Wait for the right path and then attack because he's not missing."
And clearly the advice worked when Federer won three straight games to bring the match to the tiebreak.
At his postgame press conference, Federer was asked if the board helped.
And he said, “Absolutely, look at the result. We did it.
“I like his clarity in his advice. It reminded me of the Prague match against Nick.
“It was a baseline fight trying to find the right balance of how aggressive to play.
“What I really like about Rafa, our ideas usually align. When it comes to rally points, he is excellent.
“He knows how much is enough and how much is too much. And he's a big problem, solution finder.
"I found it quite impressive in doubles when I played with him, as he is constantly looking for a new way to win or stay on a certain track if he feels he is winning.
“That's the real reason he's the champion he is today. Because he's not afraid to change a winning tactic and he also believes in resting a lot, and I do similar things.
"So it's very nice to hear you talk, especially during the game."
Federer will seek to show his own coaching talent when Nadal plays his first Laver Cup match tonight.