Lucas Joao opened the scoring for the home side with Jose Semedo doubling the advantage. Ryan Tafazolli gave the visitors a lifeline on the stroke of half-time, but a third goal from Kieran Lee and a fourth added by Modou Sougou secured the Owls’ safe passage.
Wednesday opened the scoring in the 12th minute when Alex Lopez’s free-kick found Joao unmarked at the edge of the six-yard box and he headed past Mansfield goalkeeper Scott Shearer.
Shearer was beaten again seven minutes later when Sougou’s superb inswinging cross found Semedo, who ghosted in between two Mansfield players to head the ball home.
The visitors pulled one back just before the interval when a corner from Adam Chapman was met by the head of Tafazolli, who powered his header into the roof of the net.
The home side’s third goal came in the 53rd minute. Joao’s perfectly weighted through-ball put Lee through on goal and the midfielder showed composure to slot the ball beneath the onrushing Shearer.
Wednesday wrapped up the victory in the 83rd minute when Sougou met Jeremy Helan’s low cross.