Yet the Yeltz made the perfect start and took the lead after just 17 seconds when Jamie Molyneux burst down the centre and blasted past Bedworth goalkeeper James Fogg to put Halesowen ahead straight from the kick-off.
As the lively start to the game continued, Alex Troke's half volley was well saved by home goalkeeper Dan Platt in the 2nd minute and Platt then collected a low shot from Lewis Noon in the 11th minute.
Molyneux had another couple of goal attempts for Halesowen midway through the first-half but plucky Bedworth refused to lie down and ended the first half strongly as Lewis Noon's 34th minute free-kick was scrambled away from Will Harris in the danger area.
The Greenbacks then equalised after 37 minutes when Halesowen failed to clear Bedworth's pressure, allowing Troke to place the ball past Platt from 15 yards.
Just before the interval, Halesowen's Aaron Gilpin cut inside to fire wide after 39 minutes and at the other end, central defender Kieran Morris denied Chekaine Steele in the 43rd minute.
Molyneux had further efforts for Halesowen at the start of the second period and Sam Griffiths planted a header wide from Enock Ekongo's dangerous 70th minute cross from the right. But in reality Halesowen lacked composure and never looked likely to build on their promising early lead.
Bedworth pushed on to take the lead in the 75th minute when Troke slammed home from the penalty spot after Asa Charlton was penalised for fouling substitute Lewis Collins.
Halesowen's agony was piled on with a comedy of errors in the first minute of injury time after goalkeeper Platt slipped when trying to control Ekongo's back-pass and only succeeded in letting in Steele to slot home Bedworth's third goal and hand the Greenbacks their unlikely best win of the season.
Halesowen Town: Dan Platt; Enock Ekongo, Sam Griffiths, Ivor Lawton, Kieran Morris (c), Asa Charlton, Aaron Gilpin (Kartel O'Neill-Martin 66), Aaron Birch, Lee Hughes (Isai Marseliaa 77), Jamie Molyneux, Jack Kelly. Subs Not Used: Joe Fitzpatrick, Samir Nabi, Callam Mendez-Jones.
Bedworth United: James Fogg; Richard Platt, James Hancocks, Will Harris, Ricardo Dudley, Elliot Parrott (c), Chekaine Steele, Barry Fitzharris, Levi Rowley, Alex Troke, Lewis Noon (Lewis Collins 70). Subs Not Used: Edry Moore, Jamie Lenton.
Referee: Oliver Mackey Attendance: 502