McKee was into everything and his game-high 29 points spurred the visitors to a bustling, hustling 93-91 victory.
Wollongong outmuscled the Breakers late in the fourth quarter to snatch the lead then hold it in the desperate final seconds.
It marked the Breakers' second home loss this season and left their record at seven wins and seven losses, a poor return for a team tipped pre-season to go all the way.
Wollongong trailed for much of the match but simply refused to go away, then launched their bid late in the piece after McKee's heroics had helped keep them in the contest.
Breakers veteran Tony Ronaldson said the manner of his team's defeat was unacceptable.
Ronaldson contributed 12 points to hit the 10,000-point mark in his 20th league season, but he was in no mood to dwell on that.
"That was heartbreaking and it was unacceptable," he told Radio Sport.
"We can't allow teams to kill us on the boards like that. This competition is too close to mess around for 35 minutes then expect to play for five.
"We had chances to shut them out of the game and we kept on letting them get back in."
The Breakers led 51-44 at halftime then 87-80 with four minutes remaining before Wollongong clawed their way back.
McKee had scoring support from David Gruber with 16 points, and Larry Davidson with 13, but it was McKee who most troubled the Breakers defence.
"We just crumbled," Ronaldson said.
"It was disappointing; we were outplayed and outhustled."
The Breakers' top scorer was Kirk Penney with 23 while CJ Bruton was strong in the second half for his 22 and Rick Rickert matched Ronaldson's 12.
