The attacking midfielder, who arrived from Barcelona in July, scored Stoke's second goal following Peter Crouch's opener - which came after just 19 seconds - and had a hand in the third for Jonathan Walteras as the hosts went into half-time with a commanding 3-0 lead at the Britannia Stadium.
Bojan then found the net for a second time only for the goal to be ruled out after Mame Biram Diouf was deemed to have interfered with play from an offside position.
That swung the momentum in the favour of Arsenal, who set up a tense finish with a penalty from Santi Cazorla and an Aaron Ramsey volley.
But the dismissal of Calum Chambers 12 minutes from time effectively sealed success for the hosts.
Welshman Hughes was angered by referee Anthony Taylor's decision to disallow Bojan's second but had nothing but praise for the 24-year-old.
"An outstanding second goal by Bojan, who once again has put in a really impressive performance," Hughes said.
"I think since he's come back into the side he has played four or five games and I think he has been our man of the match in every game he's played since he's come back.
"He's playing exceptionally well, he's showing everybody that not only is he a good player technically but in terms of his work rate and what he tries to do for the team he's very much a team player as well and we're reaping the benefits of that.
"He's integrated very, very well because he's a good personality as well, works hard every day to get better and works hard for the team.
"[It was a] really disappointing decision of the referee to chalk out an outstanding individual goal by Bojan, created by himself. You really should look to encourage positive play rather than look for a reason to penalise us.
"So we've gone from a situation where we could have been 4-0 to the good, that puts a spring in their step and very quickly we're looking at 3-2 and we're hanging on when the game should have been dead and buried.
"But we've got ourselves together and for the most part we saw it out quite comfortably."
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