The world’s most expensive player limped out of the action before the half-hour mark and went straight down the tunnel to join an already lengthy queue to the PSG treatment room.
He was replaced by Pablo Sarabia, but without the Brazilian the visitors ground out the victory after the break in a game that mercifully passed without incident despite the backdrop of ongoing diplomatic tensions between Turkey and France.
The result allows PSG, last season’s beaten finalists, to get off the mark in Group H, a week after they started with a 2-1 home defeat at the hands of Manchester United.
Kean, who is on loan from Everton, had already opened his PSG account with a brace against Dijon in Ligue 1 last weekend and the Italian forward put Thomas Tuchel’s team in front in the 64th minute behind closed doors at the Fatih Terim Stadium.
Kylian Mbappe played the role of provider with a corner from the left that was headed home from six yards by the unmarked Kean.
Beaten 2-0 away by RB Leipzig on their Champions League debut after winning a first Turkish title last season, Basaksehir had come close to taking the lead in the first half.
Their skipper, the Bosnian international Edin Visca, twice narrowly missed the target from range, while PSG goalkeeper Keylor Navas made a key save to deny Deniz Turuc shortly after Kean’s opener.
The French giants had also seen Sarabia shoot over to squander a glorious chance at the start of the second half, but Kean’s opener calmed any nerves and he made it 2-0 with 11 minutes remaining.
This time a miscontrol by Mbappe fell kindly to Kean, who controlled and turned before firing past Mert Gunok to make sure of the points.