Leading 1-0 from the first leg in Paris, Lyon doubled their advantage inside four minutes when Catarina Macario found the net from close range, before PSG midfielder Grace Geyoro equalised in the 25th minute.
PSG levelled the tie at 2-2 and edged ahead on away goals on the hour mark when Lyon defender Wendie Renard bundled the ball into her own net.
"I don't think we realise what we've done yet. We played a great game collectively from start to finish," Geyoro said. "We knew we had to come here and score two goals. And we did that. We never gave up."
The second leg, originally scheduled for April 1, was pushed back due to a number of COVID-19 cases within the Lyon squad.
It was only Lyon's second defeat in 23 competitive games this season, with both losses inflicted by PSG.
PSG, who have never won the women's Champions League, will face Barcelona for a place in the final.