Second-half substitute Lucia Garcia made an instant impact to set up our captain, Katie Zelem, for the decisive strike.
The lay-off was taken in her stride by Zelem, who curled a shot beyond Lydia Williams in the PSG goal with the outside of her foot in the 66th minute.
United will now face Bayern Munich in the final on Friday evening, after the Germans beat FC Barcelona with a late winner.
FIRST HALF
Paris Saint-Germain had the best of the chances in the opening half. Nina Ngueleu came agonisingly close to opening the scoring for her side, through on goal one-v-one against Sophie Baggaley after 15 minutes - but failed to convert as the United keeper blocked her effort.