The Sky Blues' barren spell at the Ricoh Arena had lasted seven matches, but the 2-0 win achieves manager Chris Coleman's target of mid-table at the turn of the year.
Both sides struggled with injuries, with Coventry forced to field two players out of position due to the absences of Dan Fox and Elliott Ward.
Wednesday almost took advantage of the uncomfortable back-line in the tenth minute when James O'Connor's ball fell to Richard Wood eight yards from goal.
However, the centre-back demonstrated why he is restricted to a place in the back four after slicing a volley embarrassingly wide.
Coventry punished the miss a minute later when Guillaume Beuzelin played a through ball with the outside of his boot to the unmarked Clinton Morrison.
The striker fired a low-drive past keeper Lee Grant to notch his tenth of the season.
Wednesday battled and had a good chance five minutes later when the ball fell to Sean McAllister in the box, but highly-rated Sky Blues keeper Keiren Westwood produced an excellent block to deny a goal.
Owls left-back Tommy Spurr broke down the left in the 20th minute and put a dangerous effort into the City box only for Marcus Tudgay to fluff his effort wide.
Coventry continued to sit back and Wade Small came close twice in two minutes for Wednesday.
In the 55th minute his half-volley from the edge of the area whizzed past the post, before his shot inside the area produced another good save from Westwood.
The chances sparked the Sky Blues to life and after Grant tipped a Michael Doyle cross away from the feet of Leon Best, Michael Mifsud fired in a bouncing shot for the Owls number one to push wide.
As the clock ran down, Wednesday committed more bodies forward and were punished by an 82nd minute counter-attack.
Best received the ball deep in opposition territory and after laying the ball off for oncoming Robbie Simpson, the former non-league star placed a low shot into the corner of the net.