The first half proved to be a frustrating one for Halesowen after failing to convert their superior possession into goals.
A 7th minute corner from Robbie Bunn led to a goalmouth scramble but the visiting defence cleared.
Bunn then headed James Bowen's 10th minute cross wide and Bowen shot at goalkeeper Dan Green three minutes later with plenty of home pressure.
Lively Montel Gibson held the ball up for Simeon Cobourne to drag a shot wide on his Yeltz debut in the 30th minute but Halesowen's moves often broke down on the edge of AFC Dunstable's penalty area.
The ODs only attempt of the first period came in the 31st minute when Taylor Rhiney fired a weak 25 yard free-kick straight at home goalkeeper Brendon Bunn.
As the chances piled up, Ashley Sammons found Reece Hewitt in space after 32 minutes but he fired his effort over the bar.
Towards the interval Bowen found Gibson but he also struck over the bar and Cobourne's 40th minute tricky run down the left ended with his angled shot cleared off the line.
At the start of the second half Hewitt fed Cobourne but he hit over the bar and a 55th minute long range shot from Sammons also flew too high.
The Yeltz went closer still in the 57th minute when Cobourne cut the ball back for Hewitt, only for defender Newman Carney to make a brilliant headed clearance off the line.
However, the Yeltz finally broke the deadlock in the 63rd minute when Hewitt set up BUNN to strike a 15 yard low shot through goalkeeper Green in a sweeping move forward.
Green then made a good 68th minute save from Gibson and made a fine 77th minute fingertip save after Gibson turned his last man.
Andy PARSONS prodded home near the post to deservedly double Halesowen's lead in the 85th minute after substitute Jamie Molyneux headed on a corner.
The visitors became more adventurous late on and substitute Joshua Crawley's 86th minute effort was turned around the post by Brendon Bunn.
Halesowen Town: Brendon Bunn; Jamie Ashmore (Jamie Molyneux 83), James Bowen, Jordan Piggott, Paul McCone (c), Andrew Parsons, Ashley Sammons, Robbie Bunn, Montel Gibson, Simeon Cobourne (Lewis Wright 87), Reece Hewitt (Luke Yates 83). Subs Not Used: Rob Evans, Josh Hawker.
AFC Dunstable: Dan Green; Kyal McNulty, Luke Abraham, Ryan Frater (c), Newman Carney, Martell Powell (Ashton Grant 70), Nick Elliot, Christian Tavernier (Joshua Crawley 70), Bernard Christie, Taylor Rhiney (Kyle Ajayi 70), Nathan Frater. Sub Not Used: Damen Pickering
Referee: Matthew Scoles