Declan Gaydon shone in the home goal with James Spooner producing several fine saves for the Bulls.
The match was marred by an altercation between the Corries' Luke Roughley and Builth Wells defender Danny Ives which saw both players dismissed with 10 minutes remaining.
Tempers boil over during Brecon Corries' goalless draw with Builth Wells. Picture by Stuart Townsend.
Action from Brecon Corries' clash with Builth Wells. Picture by Stuart Townsend.
Meanwhile fellow new boys Llanfyllin Town came out on top in a 2-1 win at Newtown Wanderers in the only other fixture.
Ryan Jones opened the scoring with a low ninth minute free-kick for the visitors with Wanderers back on terms before the break with Robbie Hartshorn heading home.