The friendly was Stoke's last before the first leg of their Europa League qualifier against Hajduk Split on Thursday, but most of Tony Pulis' first-team squad were rested having played against Brentford the previous evening.
Woodgate made his bow in Potters colours, however, while Sorensen made his first appearance of the summer following a minor back complaint.
Andy Wilkinson and Salif Diao, in central defence, also started, while Mark Wilson and Robert Huth were second-half substitutes, the latter in place of Woodgate shortly after the hour mark.
Ryan Shotton, who started up front alongside Tom Soares, hit the post early on but the hosts finished the game by far the stronger and had struck the woodwork themselves before Mekki swept home from close range nine minutes from time.
Stoke: Sorensen (Nash 46); Wilkinson, Woodgate (Huth 62), Diao, Dickinson; Marshall (Wilson 62), Arismendi, Pugh, Tonge; Soares (Stambolziev), Shotton.