The Owls replied through Jermaine Johnson and Marcus Tudgay but couldn't keep the Bluebirds out.
Owls keeper Lee Grant was in the action tipping over goalbound shots from Joe Ledley and Bothroyd in the opening six minutes as the Bluebirds pinned their visitors back on defence.
When Wednesday did mount an attack, Darcy Blake slid in to prevent Johnson from getting away a close-range shot.
In the 14th minute, David Marshall turned a Darren Potter free kick against the post before it was hacked to safety.
The Owls went ahead in the 16th minute when Tom Soares crossed from the right and Johnson was all alone at the far post to tap home.
Two minutes later, the Bluebirds were level when Purse was adjudged to have fouled Whittingham.
Picture slideshow from Jon Candy
City's leading scorer beat Grant with a superb free-kick from just outside the area for his 20th league goal of the season.
A long corner from Tommy Spurr on the half hour found Purse unmarked at the back post but his firm header was beaten away by Marshall.
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Mark Hudson made his return after a long injury lay-off when he replaced Blake for the start of the second half while the lively Johnson made way for Leon Clarke for the Owls.
City went ahead in the 53rd minute when a 40-yard pass down the middle from Stephen McPhail found Bothroyd, who raced on to slide his shot beyond Grant.
Both sides used all their subs with 20 minutes still left and with Wednesday desperate to get back on terms it left gaps at the back for City to exploit.
But it was the Owls who struck in the 78th minute when Tudgay slotted home from an acute angle.
Back came the Bluebirds and substitute Aaron Wildig sent Bothroyd racing through two minutes later for the winner with a blistering shot that left Grant with no chance of stopping.
In time added on, Etienne Esajas rifled a shot against the inside of the post with Marshall beaten.
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