The Mariners needed less than three minutes to hit the scoreboard on Friday in their final A-League Men home-and-away game, with Arthur De Lima giving the home side at Industree Group Stadium the lead with a headed goal.
But Klein soon took matters into his own hands, levelling the scores in the 17th minute before completing his brace in the 50th.
With finals ruled out after 15 defeats, the 12th-placed Roar (21 points) at least finish the season with a win and a four-game unbeaten streak.
They miss out on the finals for the fourth season in a row.
Brisbane coach Ruben Zadkovich admits his future at the club remains unclear, but remains proud of his side's campaign.
"I feel like I've left the club in a much better position than I've found it," Zadkovich told Paramount Plus.
"If it's the end for me, then that's football, and that's life.
"I'll be looking forward to making sure that my dreams and aspirations aren't hindered by the lack of belief of others."
Defending champions and premiers Central Coast farewell Kaltak sitting 10th (26 points) with their 10th defeat of the season.
The 31-year-old has yet to lock in his future, having indicated aspirations to play in Asia.
Kaltak leaves the Mariner after playing an instrumental role in their historic treble chase last season.
The Vanuatu captain quickly became the rock at the heart of the Mariners' defence after signing his first professional contract in 2023, having joined the ALM outfit as an injury replacement.
Playing 101 games in all competitions, Kaltak boasts two championships, a premiership and an AFC Cup in his CV.
Central Coast could drop to 11th if Wellington (24 points) defeat last-placed Perth Glory (14) on Sunday.
"We just took our foot off the gas a little bit and for the life of me, I don't know why," Mariners coach Mark Jackson said.
"We spoke about, at half-time, getting our intent a little bit more, when the ball goes back.
"We need to have the ball. I was a centre-half myself, so it pains me even more."
Mariners striker Alou Kuol fluffed a golden opportunity in the 33rd minute, failing to put on the finishing touches with his non-preferred left foot in front of an open goal after burning off defender Lucas Herrington and goalkeeper Matt Acton.
Central Coast's 17-year-old star Haine Eames forced two superb saves in the opening half from Acton after slicing shots through the congestion in the box.
Eames's 82nd-minute attempt beat an outstretched Acton, only to be denied by the post.
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