Both sides knew before kick-off that a win would send them second behind West Brom and into the automatic promotion places, and Stoke are now assured of a play-off spot at the very least.
The Potters went ahead in the 14th minute when Sidibe headed in Liam Lawrence’s beautifully flighted free-kick from the right.
The home side were enjoying the lion’s share of possession and Sidibe doubled Stoke’s advantage 10 minutes before the break when he latched onto Ricardo Fuller’s flick-on and burst clear before coolly slotting home.
Dele Adebola pulled a goal back when he flung himself at Michael McIndoe’s 67th-minute corner and sent a rocket of a header into the back of the net.
But Stoke held firm.