Effectively, Clontarf looked doomed to failure, however replacement out-half Martin Dufficy had a different idea.
Brought on for Peter O'Brien after 57 minutes, Dufficy was the spark that 'Tarf needed to unsettle the Cork Con defence.
After scoring a tricky penalty in the 71st minute, Dufficy used his strength and pace to carry the ball alone and breaking through two tackles, he managed to make it over the line for 'Tarf's second try which he duly converted.
However, as the try came on the stroke of full-time, the home side simply did not have enough time to complete what would have been a heroic comeback.
Speaking afterwards to IrishRugby.ie, Cork Con coach Brian Walsh said: "I thought Dufficy did a good job when he came on. He got the pace of the game up for them and he took the ball to the line, he got a good try and gave them the cutting edge. So we're just delighted to get out of here with the win.
"We kind of knew coming up here that anybody in Clontarf's position were going to target the home games. And it's always difficult here at Castle Avenue, Clontarf are a good physical side.
"The game swung to and fro, I thought we played some good rugby in the first half, we scored a good try in the second half and it's great to come here and win but we've a lot of stuff to work on.
"For both sides this weekend, it was about getting the momentum back, trying to get a win and hopefully get into the run of games for the last few weeks."
Walsh, who has guided his side to two AIB Cup successes, commended the performance of the Leesiders' back row which was without the services of flanker Billy Holland who was on duty for Munster in their Magners League defeat of Edinburgh.
"I thought the back row played exceptionally well. On a sticky pitch when the game wasn't flowing, you'd expect a lot of ball to be contestable and I don't think there was one penalty today for not releasing the ball on the ground which means that actually both back rows did their job very well," he added.
Cork Con now find themselves one point clear of their upcoming opponents Shannon with one game in hand. Walsh was positive about his side's healthy position in the league.
"On the run-in, we play Shannon, Dolphin, St. Mary's and we've got our game in hand against UL Bohs. But essentially the league is in our hands and that's where we want it to be."
On the other hand, Clontarf's director of rugby Bernard Jackman sees his side in a considerably different position.
They are second-from-bottom, six points behind Garryowen who have a game in hand. Yet, the Leinster hooker remained upbeat about 'Tarf's chances of avoiding relegation.
"I think we have a chance of being okay because we did salvage a point," said Jackman.
"We made some silly errors that cost us dearly and Cork Con are a class side and they took advantage of those mistakes but I believe that we have a team that can stay up.
"Dufficy did make a difference. We were planning to use both Dufficy and Peter O'Brien. It was Peter's last game for us, he has been a great stalwart to the club and he deserved a start.
"The idea was that Dufficy would give us a bit of a different style when he came on and the gaps opened up for him in the second half and he took advantage of it."
After a poor performance in the scrum against Dolphin in their last AIB League game which they lost 17-0, Jackman was satisfied with a huge improvement from the 'Tarf eight.
"Scrummaging was much improved and the forwards in general were looking to play which is always good. At least now we know we have a team that wants to fight for it, so that's the starting block."