The reigning champions quickly found themselves on the back foot against Marco Silva's side, and Andreas Pereira fired the visitors into the lead after 26 minutes.
A double either side of the interval from Mateo Kovacic saw City retake control at the Etihad, and Jeremy Doku added a third in the closing stages to seemingly put the result beyond doubt.
Fulham kept fighting however, and Rodrigo Muniz halved the deficit but an equaliser would ultimately elude them.
After the full-time whistle Guardiola walked over to Traore and could be seen animatedly gesticulating as he conversed with the former Spain international on the pitch.
Former Premier League striker Robert Earnshaw shared the clip on social media and detailed his view on the interaction.
'Pep Guardiola loves football so much that after Traore kept missing chances he went over at full time to coach the opponent player.' Earnshaw wrote on X.
With the score at 2-1 after the hour mark, Traore — who was linked with a move to City during his time at Wolves — had a golden opportunity to put the Cottagers level.
A deft one-two with Raul Jimenez saw him bounding towards goal and Traore immediately utilised his blistering pace to leave City defender Kyle Walker in the dust.
However, after finding himself one-on-one with Ederson inside the City box, Traore's finishing let him down and the Brazilian made a comfortable save to defend his side's lead.
City ultimately secured all three points courtesy of a Mateo Kovacic brace and a goal from Jeremy Doku
A graduate of the famed La Masia academy, Traore emerged through Barcelona's youth ranks while Guardiola embarked on his all-conquering run as manager of the club's first team.
However, Guardiola departed the Blaugrana for Bayern Munich in 2012 and Traore was handed his senior debut for the Catalan giants by Gerardo Martino the following year.