The match was postponed until Wednesday after both teams walked off the pitch and refused to return following accusations that the fourth official, Sebastian Coltescu, had used a racial term to identify assistant coach Pierre Webo, who is from Cameroon, before Webo was sent off at Parc des Princes by Romanian match referee Ovidiu Hategan.
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UEFA replaced the match officials and launched an investigation into the incident.
When the teams came out of the tunnel on Wednesday, players and the new group of officials gathered around the centre circle, knelt and raised a fist for a few moments before taking their positions and resuming the game in the 13th minute. The players also wore "No to racism" T-shirts during the warm-up.
Making up the revamped officiating crew were referee Danny Makkelie of the Netherlands, along with fellow Dutchman Mario Diks and Poland's Marcin Boniek and Bartosch Frankowsky.
Mbappe after the match said the time was right for players to take action against racism.
"Of course, I am proud of what was done. A lot of things were said but in fact, there's nothing better than actions," the 21-year-old France international said.
"We are tired, we don't want to go through this [racism incidents] again. We're all human beings and this was intolerable. People are fed up and we had to do something.
"Yesterday we were not disappointed not to play. We made that decision. We were proud. The more you let these things slide, the more you're led to believe that it's normal. But no, it's not normal."
PSG manager Thomas Tuchel said the events of the past 24 hours were more important than sport.
"We didn't want to force the team to focus on sport. We had already prepared for the game the day before," Tuchel said.
"We realised that it was necessary to understand what had happened, and to show respect for every player's feelings and opinions.
"It was an important situation for the team. It shows that some things are more important than sport."
Basaksehir coach Okan Buruk praised the players' unity in their response, as well as UEFA's decision to suspend the game and restart it on Wednesday.
"They did something good here, they helped us and it was something good," Buruk said. "We showed the entire world that we are united."
Taking a knee was popularised by San Francisco 49ers quarterback Colin Kaepernick in 2016 and gained steam as an anti-racism protest following the death of George Floyd, a Black man who died in police custody in Minneapolis in May.
Two banners carrying anti-racism messages were placed in the Auteuil tribune of the Parc des Princes stadium. The first one read "Support to Mr Webo... Proud of the players... Against racism," with the second one saying "Paris united against racism."
UEFA had two banners of their own with both clubs' logos, reading "No to racism," one in French and the other in English.
Information from Reuters was used in this report.