Ger O'Connor's third penalty of the game closed the deficit to 11-9, early in the second half, but Cashel broke through for three further tries to close out a very encouraging victory.
It was particularly so, given that they lined out without some of their key players due to injury. The result is a reversal of last year's Round Robin result between the sides.
Monivea scored a 14-8 victory back then on the way to reaching the play-offs, and they can console themselves with the fact that they also lost their opening game in last year's Qualifying Series.
The Galway outfit are now preparing for next weekend's Heineken Connacht Junior Cup final against Corinthians, while Cashel can do their homework on Navan, their next opponents in the Round Robin, who are contesting Sunday's AIB Junior Cup final.
Navan required an injury-time penalty from Karl Manning to overhaul City of Derry right at the death at Balreask Old last Saturday.
The Meath outfit led 14-11 at half-time but Derry, unbeaten during their Kukri Ulster Qualifying League campaign and through to both the Towns and Junior Cup finals, rallied to take the lead through scrum half Andrew Semple and then place-kicker Mark O'Connor.
Navan had the wind in the first half and edged ahead early on thanks to a well-taken try by winger Simon Horgan, who picked up a dropped pass and raced over from 70 metres out.
Derry's forward grunt got them back level at 5-5 when Bob McKillop drove forward and offloaded for the supporting Mark Walker to touch down to the right of the posts.
Place-kickers Manning and O'Connor traded penalties as a stop-start first quarter came to a close. Manning then kicked the hosts into a 8-5 lead before their former captain Bernard Smyth was sin-binned for going offside as David Witherow threatening the try-line.
O'Connor landed the resulting penalty kick but right on the stroke of half-time, Manning converted another penalty chance to give Navan their interval advantage.
Like the first 40 minutes, the second half was full of tension but Semple took some of the pressure off his side when he blazed over in the corner for a try, following a series of attacks down the blindside.
The try went unconverted and Derry winger Josh Lewis was close to touching down before Manning kicked Navan ahead again, at 17-16.
With five minutes of normal time remaining, O'Connor punished a Naven offside by kicking a central penalty and nudging Bevan Lynch's men back in front.
However, a ruck infringement allowed Manning land the deciding penalty and Navan's nerves jangled when O'Connor was narrowly off target with a last-gasp drop goal attempt.
AIB LEAGUE QUALIFYING ROUND ROBIN SERIES:
Saturday, March 28 -
Monivea 9 Cashel 28, Castle Grounds
Navan 20 City of Derry 19, Balreask Old
Saturday, April 11 -
Cashel v Navan, Spafield, 2.30pm
City of Derry v Monivea, Judge's Road, 2.30pm
Saturday, April 18 -
Cashel v City of Derry, Spafield, 2.30pm
Navan v Monivea, Balreask Old, 2.30pm