Manuel Pellegrini's team fought back to claim all three points in France - with Parrott once again the difference maker - on the back of scoring the winner against Real Madrid last week.
Goals in back-to-back games will be huge boost for Parrott's confidence and he labelled the goal at the Stade Pierre-Mauroy as 'very special' on his UCL debut following a summer move from AZ Alkmaar.
The Dubliner rejected a transfer to England in favour of Spain, with West Ham United tracking him, and former Hammer Joe Cole believes Parrott could be on the move again if his form continues.
"It's been refreshing. He's a big star for Ireland now as well, and they're probably pinning their hopes on him.
"I don't know what the situation was for him at Spurs. Was he low on confidence? Did he get the right opportunities?
"The talent is clearly there. But, credit to him, he's gone away and developed. If he carries on in this vein, the big guns will be circling."