American Greg Whittington scored 11 points in the opening half and was also having a presence on the boards, and Sydney started the second half well to close the margin to six.
But two separate technical fouls against Whittington in less than a minute late in the third term put an end to Sydney's challenge and their season. Cotton dropped both resultant free-throws to take the margin back to 10 points and Prather dunked for two with the inbound ball on the second foul, to make it 12.
Those fouls also gave Whittington his fifth foul for the game and there was still more than three minutes to go in the third term.
When Prather dropped his 21st point less than a minute later, it was the first time he'd made it past 20 since Round 15 and only the first time since Cotton joined the club in Round 14.
The win puts the Wildcats level with the Illawarra Hawks and Cairns Taipans on 14 wins/13 losses, with all still having one game left to play.
The Breakers have completed their schedule with a 14-14 record, but hold countback advantage over Perth and Melburne United, who can also finish 14-14 with a win over Perth later in the weekend.
Illawarra host Brisbane Bullets and Cairns travel to Adelaide.
Wildcats coach Trevor Gleeson said it was probably the best his side had played this season.
"We were aggressive. We didn't start that well, but I thought we had the tempo right for most of the game.
"We were aggressive at the hole, sharing the ball and playing good defence," Gleeson said. "I thought our court awareness was good, as to who was hot and who needed special attention."
Sydney coach Andrew Gaze said the team was extremely disappointed with the way their season finished.
"We felt we had prepared really well for this game, with an opportunity to play in the playoffs," he said. "We came up against a team that was well-prepared and shot the ball well.
"They had great intensity, great passion,. Their season on the line as well and they came up with a very good win."
