The mediocrity of PSG's first-half performance at the Parc des Princes may have had their supporters fearing another in a long line of disappointing results down the years in the Champions League knockout stages.
But Mbappe, who is expected to leave the club at the end of the season when his contract expires, broke the deadlock from close range just before the hour mark. Bradley Barcola's well-taken goal in the 70th minute then made it 2-0 to give the French champions a comfortable cushion to take to Spain for the return early next month.
There was big pressure on PSG coming into this tie after they had gone out in the last 16 of the Champions League in five of the last seven seasons.
Another early exit from the competition this season would be a monumental setback for the Qatar-owned club, especially as Real Sociedad were appearing in their first Champions League knockout tie in two decades.
They also made the trip to Paris having failed to score a goal while failing to win any of their last four games in all competitions. In addition to that, they were missing captain and top scorer Mikel Oyarzabal as he recovers from injury.
PSG, who gave a Champions League bow at left-back to 20-year-old Brazilian January signing Lucas Beraldo, were aiming to extend a run of 16 games unbeaten in all competitions stretching back to early November.
However, an early shot by Mbappe that was beaten away by visiting goalkeeper Alex Remiro was really the only time they threatened in a poor first-half showing. Instead it was the away side, winners of their group ahead of Inter Milan, who looked more comfortable and who came closest to scoring prior to the break.
In the final minute of the half, captain Mikel Merino controlled the ball before crash
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