The young Potters were made to work for their victory against a competitive Albion side with Trialist A, James Alabi and Tomi Adeloye all getting their names on the scoresheet for City.
The result leaves Glyn Hodges' side with one remaining pre-season friendly left against Rhyl on Saturday afternoon before they kick-off their league campaign a week on Monday when they travel to Aston Villa.
City made a bright start to proceedings at Wincham Park with Trialist A making a number of jinking runs just behind frontman James Alabi, before the powerful forward himself prodded just wide when stretching to reach Joel Taylor's rasping cross to the far post.
The Potters looked comfortable in possession against the non-league outfit without really troubling their opposition and they were almost made to pay for failing to be ruthless in front of goal when the home side nearly grabbed the game's opener on 28 minutes as Sam Barnes rattled the crossbar from a deep Daniel Andrews cross before Ben Harrison did likewise from the follow up.
A moment of quick thinking by Andrews almost put Albion ahead moments later when Dominic Kurasik was called into action to divert the attacker's 20-yard free-kick onto the post and away to safety as the Australian's goal lived a charmed life.
Despite the hosts experiencing a period of dominance, the Potters always looked dangerous on the break with the pace and trickery of Joel Taylor and Trialist A, and the latter's perseverance was rewarded in the 38th minute when he weaved his way to edge-of-the-area before firing an exquisite effort into the bottom corner to leave the 'keeper with no chance.
However, City's lead was short lived as less than 60 seconds later former Barbados international Neil Harvey drew Albion level in controversial circumstances when prodding home past the onrushing Kurasik following the referee's decision to overrule his assistant who had flagged the forward offside.
It wasn't to stop the Potters from heading into the break in front though, as Hodges' side retook control of the game on the stroke of half time when Alabi fired home from close range following Trialist A's run and shot was deflected onto the post and into his path.
Alabi was proving to be a tough man to mark and he continued to cause problems in the second period as he brushed off the challenge of a defender before bursting to the byline and seeing his pass across goal fired just wide by Taylor.
Albion were never going to lie down and let City dominate and they pulled themselves back on level terms for a second time eight minutes into the half when Mason Watkins was dispossessed of the ball and Andrews made the defender pay by driving an effort past the helpless Kurasik from just inside the box.
Adam Thomas, Ben Barber and Alabi all had good chances to put Stoke ahead for a third time in the contest, before substitute Adeloye did find the back of the net when Thomas' free-kick came back off the crossbar and Alabi chipped the ball across goal to his strike partner who headed in from close range.
The home side fought hard to try and find an equaliser in the remaining 21 minutes and despite Scott Bakkor firing just wide of the far post from the corner of the area, City were able to comfortably see out the game and claim the win.
Stoke City: Kurasik, Barber, Coulson, Watkins, Cook, Taylor, Ward, Trialist A (Adeloye 45), Shenton, Thomas, Alabi.
Meanwhile, City's Under-18s recorded a 4-0 victroy over their counterparts from Chester City on Tuesday afternoon at the Clayton Wood Training Ground.
A brace from Tom Shephard, Freddy Yao and a trialist sucured an emphatic triumph against the non-league club for John Perkins' charges.