The hosts produced some exhilarating passing football in the first half and took the lead on 13 minutes when Reid played a one-two with Josh Brownhill on the edge of the box and ran through unchallenged to beat Joe Wildsmith from close range.
It was 2-0 on 35 minutes, Reid this time exchanging passes with Marlon Pack before firing past Wildsmith from a narrower angle with his left foot.
Wednesday fans were already fearing the worst and their team’s fragile defence was breached again two minutes before the break, Jamie Paterson’s clever flick putting Brownhill in to shoot past the unprotected Wildsmith.
Reid completed his treble from the penalty spot on 62 minutes, sending Wildsmith the wrong way after Joel Pelupessy had needlessly tripped Pack inside the box.
It completed an emphatic win for City against a Wednesday side that failed to do justice to the supporters who made the long journey from Yorkshire.
The visitors had their chances in the first half, Atdhe Nuhiu firing over on 32 minutes and Lucas Joao shooting narrowly wide just before the interval.
But City had other opportunities, with Wildsmith saving at full stretch from Famara Diedhiou, who also volleyed over from the edge of the box.
Lee Johnson’s men had led Sunderland 3-0 at half-time last month only to draw 3-3, so Ashton Gate fans were taking nothing for granted at the break.
Having introduced Tom Lees for Daniel Pudil, Wednesday began the second half on the front foot, with Adam Reach shooting wide and Nuhiu heading over.
But any lingering doubts about the outcome were erased by the penalty, although Wednesday’s 1,400 travelling fans refused to be cowed and kept up the volume from behind one of the goals.
City might have scored another on 71 minutes when Reid put Korey Smith through, but the midfielder’s powerful shot was saved by Wildsmith.
Johnson took the opportunity to rest Reid on 77 minutes and the striker left the pitch to a standing ovation, having netted the first hat-trick at Ashton Gate since Aden Flint’s against Walsall in May 2015.
Wednesday had a chance to reduce the arrears when substitute George Boyd fired over the angle of post and crossbar from Reach’s pass on 86 minutes.
But by then City were coasting towards a result that put them back in the Championship play-off zone after a lean spell.
It was only their second win in 11 league games, but with several players returning from long-term injury, including right-back Eros Pisano, who played for 63 minutes on his comeback in this game, the outlook looks brighter.
Bristol City: Fielding, Pisano, Flint, Magnusson, Bryan, Brownhill, Smith, Pack, Paterson, Reid, Diedhiou. Subs: Walsh, Steele, Eliasson, Kelly, O’Neil, Diony, Kent.
Sheff Wed: Wildsmith, Palmer, Frederico Venancio, Pudil, Fox, Clare, Pelupessy, Reach, Stobbs, Nuhiu, Lucas Joao. Subs: Jones, Rhodes, Loovens, Lees, Boyd, Dawson, Abdi.
Referee: Tony Harrington (Cleveland)