Broncos forward Taupau was placed on report and penalised late in Saturday's night match when he chased hard through on a bomb and his knee collected Rapana's head as the Canberra winger marked the ball.
Rapana lost the ball as a result, and Broncos second-rower Kurt Capewell picked up the ball and crossed for what could have been a match-levelling try.
However, after play was stopped for several minutes while Rapana was treated for a bloody head wound before departing on a medi-cab, the bunker ordered Taupau be penalised for dangerous contact.
Referee Grant Atkins also placed Taupau on report, saying the front-rower's hands were not near making a tackle and his contact on Rapana was of a "careless nature".
But on Sunday the match review committee decided there was no case for Taupau to answer.
It is the second time this weekend the committee has not charged a player after they were controversially penalised on field, with Canterbury rookie Jacob Preston cleared of a hip-drop tackle on Saturday.
Brisbane coach Kevin Walters was adamant after the Taupau incident that it was accidental, but would not blame the loss on the penalty.
"I wouldn't say it was controversial," Walters said.
"It's an interpretation for the referees. He has obviously been injured severely.
"But I don't see any intent from Marty for it to be a penalty. But I didn't think it had a major impact on the game and who should have won and who should have lost."
Canberra coach Ricky Stuart agreed after the match, admitting he hoped Taupau would not face a ban for the incident.
"It was an accident. I feel sorry for Marty Taupau. He didn't mean to do that," Stuart said.
"He came in, he was looking for Jordy there earlier and spoke to his parents, which was real nice to him.
"It was an unfortunate incident and those things happen in these games.
I hope he is not suspended. We are clamping down a lot on the high shots again, and I understand that.
"But what is sneaking back into the game is a lot of players laying down and staying down, and I don't blame them."
Penrith hooker Mitch Kenny was the only player charged from Saturday's matches, set to cop a fine for a high tackle on Manly second-rower Kelma Tuilagi.
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