The visitors dictated the pace for much of the first half with some neat passing play and went ahead through a Wilfried Bony spot-kick after the striker was fouled by Ryan Shawcross.
However, Charlie Adam ensured Stoke were level at the break when replying with another penalty after Victor Moses went down following the slightest of touches by Angel Rangel.
Stoke boss Mark Hughes then freshened things up with three substitutions in the second period and two of them combined for the winning goal as Jon Walters headed in an Oussama Assaidi cross.
But Monk could not hide his fury at Michael Oliver's decision to award a foul against Rangel.
"The penalty against us is a disgrace - never a penalty in a million years," he told Sky Sports.
"Even their bench couldn't believe he'd given it and he should have been booked for diving."
Adam, however, felt Stoke were worthy winners as they moved up into the top half of the table.
"Once we got to grips with the game, I thought it was a deserved victory," he said.
"Bony caused us problems in the first half but once we stopped the flow to him I thought we dominated the later period of the game."
Walters added: "It was a difficult game but we got the result we wanted.
"The boss just told me to get on and do my thing, Oussie [Assaidi] put in a great ball and I managed to get my head on it."
