A converted Edward Higgardy try gave Wales a perfect start before England hit back with a score from Northampton Saints wing Jamie Elliott when he dived over in the corner.
Wales extended their lead through the boot before Kvesic crashed over for this first of the night - at a ground where he memorably made his senior Worcester debut and became the youngest Warrior in the modern era last season.
A further score from captain Alex Gray extended the visitors lead before England got their fourth try, the impressive Kvesic jumped and caught a restart before showing a quick turn off pace to score.
The second half was a somewhat different affair, England's flowing, expansive rugby deserted them as they were pushed onto the back foot for the majority of the half.
With England camped in their own 22, they then had to cope with the sin-binning of Sale Sharks prop Henry Thomas by Irish referee Dudley Phillips. Wales soon capitalised on their man advantage, carving out space for No. 8 Ben Thomas who scored to bring the home side to within a converted try of the lead at 20-26 with ten to play.
Wales, roared on by local support, continued to push but England's defence stood firm and held out for the win.