Stoke had failed to pick up a point in any of their previous six trips to Eastlands since returning to the top flight, but ended the home side's winning start to the Premier League on Saturday.
Having soaked up what the hosts had to throw at them, Stoke took the lead courtesy of Diouf's virtuoso run and finish shortly before the hour.
The former Manchester United man broke away in stunning fashion before beating Fernandinho and Joe Hart to open the scoring.
Stoke's first goal against City since September 2012 proved crucial as Hughes' men breathed life into their season against one of the Welshman's former clubs.
For Manuel Pellegrini's side, the result represents a blow going into the international break, with the Chilean boss also seeing midfielder Fernando taken off with an apparent groin problem.
Aleksandar Kolarov then connected with David Silva's cross and saw his header drift marginally off target before Steven N'Zonzi shot high and wide to conclude Stoke's first dangerous foray forward.
Lee Mason waved away the protests and the referee was soon required to cool an off-the-ball incident between Shawcross and Stevan Jovetic that capped a scrappy opening half-hour.
Pellegrini replaced the injured Fernando with Fernandinho, before Yaya Toure clipped the crossbar with the final effort of the opening half.
As in the first half, Stoke's deep and resolute backline proved difficult for the home side to break down.
A curled effort from Toure was beaten away by Begovic, before the lively Diouf gained reward in the 58th minute when he surged forward from inside his own half and nudged the ball past Fernandinho.
Having burst into the area, Diouf tucked the ball past Hart - who will perhaps feel he should have done better - and opened his account for Stoke.
While the home side rallied, it was Stoke who had the better chances to extend their lead as Victor Moses came close to connecting with Peter Odemwingie's cross and Peter Crouch headed wide.
