The first-team trio all played a major part during an hour run out as Richard Beale's development side picked up their first victory in this season's U21 Professional Development League Two North.
Zigic fired the hosts into a fifth minute lead in stunning fashion. The towering striker brought down a high ball with his chest on the edge of the Leeds area before swivelling to fire a dipping volley beyond the reach of Eric Grimes.
It set the tone for a dominant display from Blues. Zigic went close to doubling his and Blues' advantage in the 16th minute when he forced Grimes into a fine save at his near post with a low drive from the right.
Zigic, returning from a back injury, then turned provider in the 21st minute to play in Asante who had Grimes well beaten with a well-taken finish just inside the Leeds box.
Left-back Murphy then tried to get in on the act just after the half-an-hour only to see his sweetly-struck free-kick from 25 yards rattle back off the post.
Blues continued to pile on the pressure and forced Grimes into a fine save to keep out Asante's stooping header from Koby Arthur's cross from the right.
Goal-scoring chances were limited after the break with the trio of Zigic, Murphy and Asante making way for Reece Hales, Charlee Adams and Demarai Gray on the hour mark.
Hales combined well with Arthur down the right in the 67th minute to set up Kwadwo Asamoah for a close range chance that was agonisingly diverted on to the post by Grimes.
Blues were forced to play the closing minutes with ten men on the field as the lively Scott Allan hobbled off with a niggle.
Above picture gallery courtesy of club photographer Roy Smiljanic. For a full list of Blues U21s' competitive fixtures, click here
Blues U21s: Townsend; Fry, Packwood, Kelly, Murphy (Adams 60); Higgins, Asamoah, Allan, Arthur; Zigic (Hales 60), Asante (Gray 60). Unused subs: Preston, Truslove.
Leeds U21s: Grimes, Byram, Denton (Coyle 68), Lenighan, Killock, Taylor, Norris, Parkin (Cook 60), Walters, Dawson (Stokes 79), Hall. Unused subs: Atkinson, Phillips.