Martens’ brilliant curling shot took the lead to 1-0 before she came in on the back post after half an hour.
Marie-Antoinette Katoto got one back for PSG shortly after and jumped on a loose ball in the six-yard area.
Barcelona went 3-2 in total and will play against Chelsea or Bayern Munich – who meet on Sunday – in the final.
Jennifer Hermoso hit a post minutes before Marta Torrejon’s header came off the top of the crossbar as Barcelona pushed for a third goal.
PSG pushed for the equalizer late, knowing a second away goal would help them through, but Barcelona held their own.