Bunn set up Josh Hawker to shoot straight at goalkeeper Justin Cerga in the 7th minute and Cerga beat the ball away after Bunn whipped in a 15th minute free-kick.
But the first period was a disjointed affair with the Yeltz performing below their recent standards.
Daventry's Jack Bowen headed wide at the far post after 40 minutes and home goalkeeper Bradley Catlow punched Aaron King's 41st minute corner clear.
After the quiet start, the Yeltz grabbed a 43rd minute lead when BUNN's shot from the left took a deflection to loop into the net.
In the final minute of the first period, Montel Gibson's shot earned a corner and Cerga punched clear from another Gibson chance.
But the second half was a completely different story as the rampant Yeltz tore Daventry apart with four more goals.
Ash Sammons played a lovely ball down the left of the penalty area for BUNN to smash home and increase the lead with his second goal in the 48th minute.
Just a minute later Bunn played a fine cross field ball for Isai MARSELIA to control and slam home to mark his return to the Grove.
Sammons and Bunn then made a great interchange of passes to earn a 55th minute corner and Gibson's effort was deflected for another corner two minutes later.
Cerga made a good save to deny Sammons after 58 minutes and McKauley Manning brought a good save from Cerga in the 62nd minute with Gibson planting the rebound just over the bar.
Halesowen were now in complete control and the home side made it 4-0 in the 69th minute when Marselia was brought down by Oliver Stanbridge and SAMMONS fired home a low and hard penalty.
Substitute Simeon COBOURNE latched onto a ball through the middle and slotted home with great composure to complete the scoring at 5-0 in the 80th minute.
Home substitute Jack Holmes - a recent loan signing from Burton Albion - looked lively late on and he curled just wide after 82 minutes before firing at Cerga following a good mazy run a minute later.
The Yeltz ended the game with ten men after defender Andy Parsons limped out of the game with five minutes remaining and Bradley Catlow made a good save from Bowen as well beaten Daventry went close in the final minute.
Halesowen Town: Bradley Catlow; Jamie Ashmore, Jordan Piggott, Ash Sammons, Paul McCone (c) (Andy Parsons 67), Rob Evans, Josh Hawker, Robbie Bunn (Jack Holmes 64), Montel Gibson (Simeon Cobourne 64), McKauley Manning, Isai Marselia.
Subs Not Used: James Bowen, Luke Yates.
Daventry Town: Justin Cerga; Daniel Childs (Adam Creaney 69), Jack O'Connor, Ross Harris, Kyle Barnett, Philip Cassidy (Leslie Lewis 76), Taylor Orosz (Oliver Stanbridge 65), Jack Finch, Jack Bowen, Aaron King, Aiden Print.
Subs Not Used: Matthew Finlay (GK).
Referee: Andrew Gender Attendance: 613