The Owls, who have now won nine of their last 10 meetings with the Reds, had the game wrapped up by half-time.
Rhodes had completed his treble by the 37th minute - capping it off with a superb overhead kick - while Steven Fletcher added a fourth in first-half injury-time.
It was the worst defeat of Sabri Lamouchi's short tenure as Forest manager, and it was enough to lift Garry Monk's side above their hosts and into fifth in the Championship table.
Barry Bannan flashed a low shot wide for the visitors in the opening seconds.
Cameron Dawson was forced into a save at the other end, but it was a simple one, as Sammy Ameobi ended a twisting run with a weak shot.
It was Brice Samba who was beaten in the ninth minute as Wednesday gave their 2,000 travelling fans an early goal to cheer.
A flick from Fletcher gave Rhodes the chance to slot home a precise finish, across goal and into the far corner of the net.
Things got even better for the Owls as rampant Rhodes bagged a second four minutes later. This time it was a simple header that found the same corner of the net, following a superb cross from Adam Reach.
Forest were rocked and it almost got worse when Reach sent a spectacular dipping shot towards the far post, where it only missed the target by a foot or so, with Samba looking on.
Samba did make a solid save to keep out a volley from Fletcher, while Kadeem Harris bent an effort narrowly wide.
Joao Carvalho forced a smart save from Dawson with a bending, dipping shot. From the resulting corner, Ryan Yates looked to have been pulled to the ground in the box.
Ben Watson lifted a great chance over as his Forest team-mates appealed for a handball in the box, but his side's wait for their first penalty of the season continued.
Rhodes completed his hat-trick in the 37th minute as Forest failed to clear a corner, with the ball falling perfectly for the striker to apply a spectacular, acrobatic finish.
Ameobi came close with a curling effort that was well saved before Matty Cash came less close with a wild shot, as Forest looked for a route back into the game.
But it was the Owls who added a fourth in injury time. Forest failed to clear another corner and the ball dropped kindly for Fletcher to scramble home his 12th goal of the season.
It was damage limitation time for Forest in the second half.
Cash came close with a powerful long-range effort that dipped over, while Watson's bouncing shot was easily held by Dawson.
Ameobi was also a whisker away from a consolation goal when his shot was deflected inches wide.