Summerhill produced a highly efficient display when they needed it most to beat Moynalvey and advance to a preliminary quarter-final.
The reigning champions will play Seneschalstown with the date, time and venue to be announced.
This was the first meeting in two years between the two neighbours. In August 2012, the end result was the same as Summerhill beat Moynalvey by 1-20 to 1-11.
Brian Ennis' goal was the platform to Summerhill's success as it gave them some breathing space after a competitive opening quarter. Ennis finished as the game's top-scorer with 1-8, 1-2 of which came from play.
All six starting forwards for Summerhill scored from open play.
Full-forward Gary Rispin was the first of Summerhill's front six to find his range in the first half. The five other forwards all scored in the first half as well with the other 1-5 coming from Ennis.
Ennis' goal came from a 50-50 ball around the 45 metre line which Damien Byrne won. Byrne hand-passed to Ennis who carried and shot low to the bottom right hand corner of Ray Ryan's goal.
The tempo dropped considerably in the second half as the game was all but decided. Moynalvey's woes were compounded when county star Padraic Harnan was sent off for a second bookable defence.
Ennis (three frees), David Larkin, Paul Rispin and Barry Dardis all scored points for Summerhill in the second half.
Summerhill: Tony McDonnell; Padraigh Jennings, Caolan Young, Eamonn McDonnell; Davy Dalton, Willie Ryan, Ronan Ryan; Brian Ennis (1-8, 0-6 frees) Damien Byrne; David Larkin (0-2), Paul Rispin (0-2), Adrian Kenny (0-1); Barry Dardis (0-2, one free) Gary Rispin (0-1), Kevin Ryan (0-1). Subs: Ross Ryan for D Byrne, Alan Lyons for E McDonnell, Stephen Husband for K Ryan.