Huddersfield's Danny Ward also scored two goals and created his side's other two strikes, but the impressive individual effort was overshadowed by a stunning comeback from the Bees.
Ward, on-loan from Bolton, struck with a solo effort into the bottom right corner in the 14th minute and then found the net again after Brentford goalkeeper Simon Moore fumbled his powerful drive.
Schlupp, on-loan from Leicester, gave Brentford hope in first-half stoppage time when he raced onto a long punt from deep and slotted home.
He then levelled soon after the restart from Myles Weston's through ball but substitute Lee Novak blasted Town back in front only for Lewis Grabban to make it 3-3 on 58 minutes after Huddersfield keeper Ian Bennett mis-kicked an attempted clearance straight to him.
Ward, who has now scored three goals in two games, set-up Benik Afobe for a close-range finish on 63 minutes but Grabban levelled again when he tapped in from Schlupp's final pass.