The tie appeared for extratime before Mjelde poked home from Karen Carney’s cross to seal a 3-2 aggregate win.
Kadidiatou Diani had put PSG ahead at the night with the game’s first shot on target early in the 2nd half.
A calamitous particular goal by Chelsea keeper Ann-Katrin Berger made it 2-2 on aggregate before Mjelde won the tie.
The Women’s Super League winners will confront holders Lyon in the previous four, when they watched last year’s defeated finalists Wolfsburg 6-3 on aggregate.
Chelsea pressed but didn’t sabotage to improve their own two-goal first-leg advantage for much of the match.
The Parisians were nullified for much of a poor first half, but did show late glimpses of their skills – Diani sending a warning shot rather wide, before Marie-Antoinette Katoto had been wastefully off target.
Diani, however, sparked two-time finalists PSG to lifetime when she turned into a low Ashley Lawrence cross from 10 yards out soon following the break.
Berger’s terrible fumble because she attempted to collect a corner made it 2-0 at the evening and degree on aggregate with 3-4 minutes remaining.
PSG: Endler, Cook (Bunn 90+3), Geyoro, Katoto, Diani, Lawrence, Paredes, Berglund, Perisset (Glas 75), Formiga, Wang.
Unused substitutes: Kiedrzynek, Diallo, Zamanian, Morroni, Baltimore.
Chelsea: Berger, Blundell (Carter 74), Mjelde, Eriksson, Andersson, Spence, Ingle, Ji, Bachmann (Kirby 60), England (Bright 60), Carney.
Unused substitutes: Lindahl, Cooper, Riley, Engman.