Cooke secured a bonus point with the last play of the game against Ballymoney at Shaw's Bridge on Saturday afternoon.
Having led through a brace of tries from Andrew Pollock either side of a score from Ian Anderson, it looked as if the south Belfast side would have to content themselves with only four points, but No 8 Sam Boyd forced his way over in the final seconds to ensure a full haul.
Having flirted with a relegation battle throughout another injury-plagued campaign, Cooke are now remarkably just four points off the qualifying places for next year's All-Ireland Junior Cup.
Ballymoney, however, are mired in real trouble and, with only 15 points left to play for, Jason Taggart's side are 14 behind eighth-placed CIYMS having played a game more.
Given Ards' impending return to the junior ranks, the Kilraughts Road outfit's only real hope of avoiding relegation is now to catch Donaghadee, seven points ahead in ninth, and pray that the Qualifying One representative in the All-Ireland round-robin gains promotion.
Cooke player/coach Colin Atkinson, who came off the bench in the win, was pleased by the late effort of his side.
"I think we showed a lot of character at the start of the game to hold out and you saw that again in the end as we just kept going to get the bonus point," he said.
"Credit to Ballymoney, they threw everything at us. Sometimes when it's a relegation battle you have to win ugly and, until the last 15 minutes, that's what we were doing."
With the league standings tightening as we approach the season's final month, Atkinson stressed that there is still an opportunity for Cooke to make an impact.
"I think before we kicked off, you could see how tight it was between the bottom and the top four.
"There are teams showing that everybody can beat everybody and this win puts us in a better position."
The coach also reserved special praise for a trio of younger players, half-backs Gareth Robinson and Andrew Hanna, as well as the free-scoring Pollock.
"Our nine and 10 were playing for Wellington this time last year and I thought they were outstanding, especially young Andy Hanna," he said.
"With Andy (Pollock) I think people are surprised with the speed that he has. Everybody knows about him now though and I'm delighted to have him in the team."
Despite the final scoreline, it could have been a very different contest had Ballymoney made the most of their chances in the opening minutes.
Having secured early possession, the north Antrim side advanced into the Cooke '22' and were camped near the hosts' line.
Despite a number of penalties being sent into the corner, the rolling maul was repelled time and time again and, when the visitors were pinged for holding on, Cooke were finally able to clear.
Ballymoney would not enjoy such a sustained period of pressure again and the first points would be Cooke's after half an hour had elapsed.
A Phillip Cartmill penalty gave them a 3-0 lead and, with Neil Mullholland having already spent 10 minutes in the bin, Danny Platt was shown a yellow card shortly after.
Against 14 men, further points seemed imminent and a classy move off a scrum was initiated by Boyd, Hanna and Kyle Mitchell with the centre's offload releasing Pollock to go in under the posts.
It wasn't all going the fullback's way, however, as he was yellow-carded shortly after for infringing at the breakdown.
Ten minutes after the turn, with Cartmill having departed injured, kicking duties were handed to Hanna and the No 10 connected well to move the score to 13-0.
The attritional nature of the game cost Ballymoney both David Rea and Chris Watson to injury and, after their reshuffle, Cooke scored for a second time with Mitchell again creating the try with a clever offload that released Anderson.
A second score from Pollock with five minutes remaining ensured that the bonus-point chase was on but it was Ballymoney who scored next.
Matthew Steele went over in the left corner after good work from Mullholland and James Campbell.
Cooke were not to be denied, however, and in the last play of the game Boyd scooped up a loose ball, despite a hint of a knock-on in the build up, to go over for the all-important fourth score.