The 31-year-old record goalscorer's intricate flick from Marc Laird's angled cross on 58 minutes buried a Leeds side who had stolen the lead through Luciano Becchio's first-half wonder strike.
Argentinian Becchio scored a beauty from 22 yards with Leeds' first attempt at goal just after the half-hour when his left-foot arrow beat David Forde and nestled in the far corner.
Harris was also instrumental in Martin's 36th-minute equaliser for the dominant hosts when the winger latched onto his reverse pass before lifting it over the advancing David Lucas.
Then Harris' delicate header guided instrumental Laird's right-foot cross into the far corner leaving keeper Lucas rooted to the spot and the travelling White Army slumped into their seats.
Leeds manager Gary McAllister reacted immediately by introducing Enoch Showumni and Robert Snodgrass into a 4-2-4 formation, but the Lions remained resolute.
Lewis Grabban had a fantastic opportunity to seal the points late on having been put through acrobatically by Harris, but the winger fired straight at Lucas with a tame left-foot strike.
With three minutes left on the clock, Harris put the icing on the cake when he hammered home the Lions' third from an acute angle.
Tireless Gary Alexander pressurised Lucas into a scuffed clearance from Fabian Delph's lazy back-pass and it fell kindly to Harris, who calmly sidefooted into the unguarded net.