Spillane gave the visitors a third minute lead, planting a firm header past Richard O'Donnell from Nathan Byrne's corner.
Wednesday's Gary Madine headed over before Rob Jones equalised with a near-post header after meeting a Gary Teale corner.
Brentford regained the lead six minutes later when Lewis Grabban nipped in ahead of Jones and crossed to Schlupp who headed in from close-range.
Darren Potter put a free-kick just over as Wednesday tried to force an equaliser before the break.
Teale then saw his overhead kick cleared off the line and Madine put a low shot wide.
Wednesday substitute Jermaine Johnson threatened with a strong run into the area before trying an angled shot which went beyond the far post.
Brentford substitute Saunders completed the scoring in the 82nd minute, beating O'Donnell with a superb 25-yard free-kick which left the keeper rooted to the spot.
Sheff Wed 1-3 Brentford: Match Report - view commentary, squad, and statictics of the game as it happened.