Stoke set off as if they really meant business as Ricardo Fuller fired narrowly over from a Liam Lawrence pass in the first minute.
But Coventry, who packed five across midfield, soon closed ranks and began to gain the upper hand in terms of possession.
Stoke began to work up a head of steam as half-time approached with debutant Danny Pugh volleying wide and Lawrence having an effort blocked.
And Coventry were fortunate two minutes after the break when Ben Turner's clumsy challenge on Fuller could have resulted in a penalty.
The contest was now opening up with Stoke looking menacing, but it was Coventry who took the lead against the run of play in the 58th minute.
A poor clearance by Andy Wilkinson and the strength of Dele Adebola, who held off Leon Cort, enabled Mifsud to place a right-foot shot past Steve Simonsen.
There was controversy a minute later when Stoke believed they had equalised.
Ryan Shawcross' header from a Lawrence corner appeared to cross the line before Dimitrios Konstantopoulos saved, but the linesman thought otherwise.
Coventry took a grip of the game in the 63rd minute when Adebola beat Stoke's ragged offside trap to head in Isaac Osbourne's cross.
And it took a brilliant save by Simonsen to deny the clean through Michael Doyle shortly afterwards.
Stoke were back in it 19 minutes from time when Lawrence put away a penalty after he was tripped by Turner.
But Coventry sealed an impressive victory ten minutes from time as Doyle released Mifsud, who sped clear to hammer the best goal of the game.
Mifsud smashed a shot against a post and it also took an excellent save from Simonsen to deny Jay Tabb as the visitors threatened to run riot in the closing stages.