Striker Ishmael Miller struck either side of half-time to end the Owls' impressive away run and earned the Glovers back-to-back wins at Huish Park for the first time this season.
Yeovil came into the game buoyed by a run of four league matches unbeaten, including a heroic point at Reading last weekend despite having three players sent off.
Manager Gary Johnson was forced to shuffle the pack as a result and handed Spanish midfielder Roman Palazuelos a first start in place of the suspended Joe Ralls, while Miller returned to the starting line-up at the expense of Kieffer Moore.
Miller's return could not have come at a better time for the Glovers with a congested March fixture list ahead, and the Nottingham Forest loanee took only 10 minutes before he stung the fingertips of Owls goalkeeper Damian Martinez with a powerful drive.
Away-day specialists Wednesday, who were unbeaten in nine matches away from Hillsborough before the trip to south Somerset, hit back and came close when Jacques Maghoma's strike was palmed away by Marek Stech.
Owls striker Leon Best received a good reception from the home faithful on his return to Huish after enjoying a prolific spell with the Glovers in 2006/07, scoring 10 goals in 14 starts to fire Yeovil into the League One play-off final.
However, the former Newcastle United man endured a first half to forget with service from wingers Chris Maguire and Maghoma severely restricted by a resolute Yeovil defence.
In contrast, Miller saw plenty of the ball and nearly notched the game's opener on 15 minutes when he combined with James Hayter to fire home, but was denied by the linesman's offside flag.
Wednesday slowly found their feet in the Somerset sunshine and could have snatched a lead when Giles Coke's effort looked goal-bound, but cannoned off Glovers defender Shane Duffy and out for a corner.
However, the relentless Glovers finally forced a deserved breakthrough three minutes before the break when Miller latched on to Tom Lawrence's flick to rifle the ball home.
The 1,569 travelling Wednesday fans expected a much-improved display from their side in the second half, but their hopes were dashed inside six minutes when Miller angled an unstoppable 20-yard strike into the top corner.
The visitors turned to substitute Jermaine Johnson to rescue the game - and despite looking lively down the right flank, the tireless hosts kept the backdoor firmly closed.
Wednesday almost reduced the deficit in the final 10 minutes when Glenn Loovens headed over, but their torrid afternoon was completed moments later when Sam Hutchinson was sent off for a second bookable offence.