The Serie A side dominated the match against the Baggies and, after spurning numerous chances, finally took the lead when Francesco Lodi's shot deflected off Shane Long and flew in
The Premier League outfit hosted their Italian opposition at Telford's New Bucks Head stadium, with an own-goal from Shane Long enough to seal the result.
West Brom boss Steve Clarke named a strong side, including in-form Nicolas Anelka, Youssouf Mulumbu and Claudio Yacob, while Alberto Gilardino lined up for the visitors, fresh from representing Italy at the Confederations Cup.
Genoa had the best of the opportunities in a quiet opening period. Andrea Bertolacci flicked a clever effort just wide from Mario Santana's cross and Juraj Kucka's 25-yard free kick was smartly parried over by Luke Daniels on the stroke of half-time.
A raft of changes at the break saw home captain Chris Brunt and Long introduced as Clarke went in search of a winner, and the second period began in exciting fashion.
Kucka again went close, curling just wide after Kemar Roofe gifted possession to the Slovakian, and a minute later Graham Dorrans saw a stinging drive parried away by Mattia Perin in the Genoa goal.
The Italians kept the pressure up as Santana volleyed wide, but they were finally awarded for their pressure 20 minutes from time as Francesco Lodi's strike was deflected past a helpless Daniels by Long.
West Brom looked for a way back into the match, but academy prospect Wes Atkinson's low effort was easily saved and they created little else of note on a difficult evening.