Bourneview Mill managed to break the deadlock but struggled to protect the advantage at Dungannon Tigers.
Stephen Elliott’s header helped the visitors claim control in difficult conditions.
However, Tigers regrouped to level courtesy of a free-kick before moving in front off a deflected effort.
“It was frustrating, especially after taking the lead,” said Bourneview Mill’s Mark Jackson. “We worked hard overall.”
BOURNEVIEW MILL: David Crawford, Jeff McClure, Steven Haugh, Gavin Fox, Dale Compton, Mark Boyce, Chris Traynor, Gary Hill, Stephen Elliott, Geoff Neill, Ciaran Dickson, Thomas McClelland, Kyle Abraham, Tony Murray.