Tullamore were beaten in Mullingar on St Patrick's Day.
Mullingar are the last midlands club left standing in the Towns Cup after the last 16 stage over the weekend.
The Westmeath club ran out 26-13 winners over Tullamore in Shay Murtagh Park on St Patrick's Day.
Elsewhere Portlaoise were well beaten 41-7 by Carlow while Portarlington were dumped out of the competition after Ashbourne beat them by 37 points, 47-10.
Mullingar will have their hands full in the quarter finals, they've been drawn to take on Wicklow who scored 13 tries and conceded no points in an 81-0 demolition of Navan at Ashtown Lane.
Kick off at Shay Murtagh Park is set for 3pm on Sunday.
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