James Bowen went on a run and got a cross in for Jamie Molyneux to head home.
After the break, Montel Gibson saw an effort chalked off and Josh Hawker saw a shot tipped over by Bedworth goalkeeper Adam Harrison.
But Bedworth came back at Halesowen and equalised on 75 minutes through Alex Troke.
Two minutes later, Ashley Sammons shot over the bar for Halesowen and on 82 minutes Lee Hughes headed a Hawker free kick over.
Bedworth had to play the last five minutes of the game with ten men after Luke Rowe was sent off.