Seeking a return to the final for the first time since 2013, the 1997 winners were dogged and determined, outmuscling their heavily favoured opponents.
Fuellkrug, playing in his first Champions League season at the age of 31, collected a lofted pass from centre-back Nico Schlotterbeck in the 36th minute and blasted a low shot into the left corner of the net.
PSG, led by Kylian Mbappe, hit the post twice in quick succession early in the second-half but could not break through.
Dortmund, who had already lost and drawn against PSG this season in the group stage, can continue to dream of a return to Wembley 11 years after their last Champions League final.
Despite the setback, however, PSG will remain confident of overturning the deficit at home next week against a side they thoroughly outclassed at their home venue in September.
Dortmund manager Edin Terzic said pre-match PSG were "built to win the Champions League" since the Qatari takeover a decade ago.
Nowhere was the contrast between the two clubs greater than PSG's global superstar Mbappe, playing in his last season for his hometown club, and journeyman Dortmund striker Fuellkrug, who was playing second-division football this time two years ago.
Spurred on by a passionate home crowd who booed and whistled every Mbappe touch, Dortmund had the best of the opening stages, Jadon Sancho shining down the right flank.
Marcel Sabitzer had Dortmund's best chance of an opener after 14 minutes, blasting straight at Gianluigi Donnarumma from a tight angle.
The opener came after 36 minutes thanks to some superb old-school forward play from Fuellkrug.
Centre-back Nico Schlotterbeck had the ball well in his own half and thought about a safe pass back to the 'keeper but instead punted it forward, with only Fuellkrug aware of the idea.
The striker controlled the ball with one touch and drilled a low shot past a helpless Donnarumma.
Fresh from wrapping up the Ligue 1 title at the weekend, PSG had few chances despite their attacking riches in the opening half, recording zero shots on target.
The visitors however sprung to life after half-time, Mbappe rattling the inside of one post seconds before former Dortmund wing-back Achraf Hakimi rattled the inside of the other.
PSG should have equalised after 56 minutes, Marquinhos curled a beautiful pass through a crowded Dortmund box but Fabian Ruiz's diving header went wide.
Another former Dortmund player Ousmane Dembele blasted over right in front with 10 minutes remaining.
The impressive Sancho laid on an excellent pass for Julian Brandt with moments left but Dortmund's hopes of a second were snuffed out by some desperate PSG defending.
The victory, along with Tuesday's 2-2 draw between Bayern Munich and Real Madrid in the other semi-final, guarantees Germany rather than England or France an extra Champions League place for next season.
That has already secured Dortmund's place in the competition next season
