The in-form Scott McCullough added to his tally of goals to help Hanover sink Ballymoney United on Saturday.
The Irish Cup victory arrived for Hanover thanks to a brace apiece by midfielder McCullough and coveted forward Justin Bradley.
Steven Douglas sparked the tie into life by breaking the deadlock at the end of a flowing team move.
Bradley’s delicate first touch then finish doubled the tally ahead of a superb free-kick strike by McCullough.
Ballymoney converted a penalty kick but McCullough’s long-range effort capped a driving run from deep.
Thai Blevins and substitute Regan McIlveen then linked up late on, with Bradley popping up inside the penalty area for the final touch to close out the scoring.