Bridgnorth got off to a solid start with the bat as openers Alex Yarnley (31) and Harry Martin (67) put on a partnership of 90 for the first wicket.
However, despite a useful 35 from Charles Thornton, other meaningful contributions were lacking from a middle order missing a few experienced names as the Cricket Meadow men finished on 198-6 after 50 overs.
Penkridge made a solid start to their run chase against a youthful bowling attack, reaching 103-1 with Sam Baugh (1-29) taking the first wicket to fall.
Yarnley (2-37) and Andy Leather (2-31) worked hard in an attempt to gain control of the visitors' reply, and Doug Roberts (1-40) returned to take a scalp of his own. But ultimately Penkridge chased down what appeared to be a below par total on a good batting wicket in the 46th over.
Bridgnorth's second string host Halesowen next weekend, when they will hope to chalk up their first win of 2014.