Goals from Josh Windass and Callum Paterson after the red card gave the Owls the three points, with Potters striker Tom Cannon also seeing his penalty saved by James Beadle.
Rohl said: “After the red of course we had to change the structure for the second half, but we didn’t want to go too defensive. We stayed offensive in the midfield because I felt if we had the ball we could hurt Stoke.
“Paterson never gives up. He has worked really hard to get minutes on the pitch and I’m pleased he scored.
“Beadle made a great save from the penalty and put in a big performance, too. Some top individual performances, but credit goes to my whole team.
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