Neither side managed to break the deadlock in normal time and 14 of the scheduled 15 minutes of extra time had elapsed when Clontarf netted the crucial goal that booked their place in round two.
Starting with their regular line-up on the Astro surface at Mount Pentle, the Doagh girls mounted early attacks in which Nikki Turkington and Kerri Erskine had shots saved.
Clontarf soon found their feet and forced three penalty corners that were cleared by Karen Barr and Claire Dundee, but during the second quarter play was mainly at the opposite end, where Parkview were unable to capitalise on a series of five penalty corners. Gail Nicholson, Susie Weir, Barr and Turkington had shots on target, but the Dublin defenders came out on top.
During the second session, Parkview had territorial advantage without making any impression on the scorecard and then in a Clontarf counterattack Sharon Gaffney pulled off a stunning one-handed save to deny a home striker who had got in behind the defence.
In extra time, defences continued to have the upper hand until the final minute, when Clontarf got the winner from close range following a right wing thrust.
Reflecting on the weekend, Emma Stubbs said: "We had a very enjoyable weekend. We travelled down on Saturday morning and returned on Sunday afternoon. The match was played in a sporting spirit and afterwards we were entertained to a much appreciated meal in a local hotel.
"We gave a good account of ourselves, but were disappointed with the 1-0 result, after having had the better of exchanges for most of the game."
Parkview Ladies: S Gaffney; L Chalmers, C Dundee, G Nicholson, E Stubbs; J Hargie, K Barr, S Weir, A Halaseh; N Turkington, K Erskine. Subs: Z Purdy, L Stephens.
This weekend, Parkview have a home Senior League Section 2 fixture against PSNI at Foundry Lane.