Twice Gary Madine came close to opening the scoring in the early exchanges, but the striker had an effort blocked by Keith Lowe after five minutes, before heading a Jeremy Helan cross over the crossbar six minutes later.
Madine had the chance to make it 2-0 late in the half, but the forward was denied by a smart save from York goalkeeper Jason Mooney.
The Owls had their second late in the first period, however, when Maguire found the back of the net from some 35 yards.
Caolan Lavery had the first real chance of the second half, but the Wednesday forward could only strike his effort straight at Mooney.
Wednesday continued to dominate in the second 45 minutes, but neither side could add to the scoring as the Championship outfit ran out 2-0 winners.