Cooke secured a valuable bonus-point win over Donaghadee at Shaw's Bridge on Saturday afternoon to ease away from the Kukri Qualifying One relegation battle.
The victory means the south Belfast side now sit eight points ahead of second from bottom Ballymoney, with Donaghadee one further back, and they will feel confident of their future in the division irrespective of whether one or two teams face the drop.
It had been a tight contest in the first half - Cooke led by just 13-10 at half time - but player/coach Colin Atkinson scored shortly after the resumption of play and his side never looked back.
Speaking after the victory, he said: "I'm absolutely delighted. It was a game that both teams desperately needed to win.
"Our boys have played well without getting the results recently but everybody really stepped up.
"There's going to be times when the opposition have a purple patch and get some points, but that's when we need to keep our heads, not panic, and focus on what we've been doing in training.
"That's what we did. We're just delighted to get the five points."
On the approach to the season's final six games, he added: "You look at this league and everyone can beat everyone, that's what's exciting about it.
"The young guys bring a lot of confidence to the team so that's the attitude we have."
The visitors were the first side to threaten in the contest when, after winning a penalty, they kicked to the corner and earned a lineout in a promising position.
Cooke managed to poach the throw but there was still a chance for Dee when the clearing kick found touch just outside the 22.
This time, Gareth Gordon's throw found its intended target but they were soon penalised for holding on when the ball went to ground.
With 12 minutes on the clock, the hosts would register the first points of the day through Andrew Pollock's score.
A searing break from Alex Gourley advanced the ball and, when the fullback was tackled, scrum-half Gareth Robinson was quick to the breakdown and his box-kick over the top was gathered by left winger Pollock, who crossed in the corner.
Gourley could not add the conversion from the sideline but Cooke doubled their tally just five minutes later.
Flanker Stephen Mooney burst upfield and, after drawing the defender towards him, offloaded to Phil Cartmill - making the start after returning from injury with an appearance off the bench last week - who still had work to do but rolled through the tackle and over the line.
The conversion was again off target and there was to be a flurry of scoring in the half's final five minutes.
First, Dee grabbed their first points when, from a scrum deep inside Cooke territory, their pack rumbled over the line and number 8 Stephen Adams was able to pick up at the base and touch down.
Again there was to be an unsuccessful conversion and, when Gourley knocked over a penalty from a central position on the edge of the 22, Cooke looked set to take an eight-point lead into the second half.
However, Dee came back once more and again opted for the scrum when their hosts were penalised near their own posts.
Several forwards had a go at forcing themselves over the whitewash but when they were continually repelled, Alistair Lockhart spread the play to Paul McKenzie whose looping pass was scooped up by Thomas Slane and the wing sprinted his way over in the corner.
Cooper could not add the extras, meaning it was just a three-point game at the turn.
The second half would prove a far less balanced affair and a Colin Atkinson try just five minutes after the restart, scored after good work from Pollock and Gourley, would prove to be a turning point.
Thereafter, Donaghadee would add just three more points - thanks to a drop goal from McKenzie - while Cooke would run in a further three tries.
With one quarter remaining, the home side were pounding away at the Dee line but looked set to get no reward before the ball was fired out to the backline.
Jonathan Kingham did well to spin out of a tackle and find Gourley with the fullback then releasing Pollock, who proceeded to grab his second score of the day.
The winger then turned provider when his fleet-footed run up the touchline had Dee tacklers grasping for air and freed Cartmill to go in under the posts.
With only minutes of the contest remaining, the versatile Brian Mannus finished off the scoring when he showed a good step and ran over untouched.