They extended their advantage to 26-13 midway through the second half after 20 minutes of clinical football.
McGarvey more than atoned for his earlier indiscretion - taking the ball to the line without fear and hitting hard in the tackle.
His try - a stunning 25m effort in which he chopped off both feet past tiring forwards before going around the fullback - looked to have shut the home side out of the contest.
Instead it stung Tauranga Sports into action. They scored a classic forward driving try from a lineout after the Mount was penalised for a breakdown infringement after fluffing the kick-off, with Morris' sideline conversion making it 26-20.
An epic defensive stand from each side followed, with the impressive Johan Bardoul saving what looked like a certain try in the dying moments.
The converted blindside try to Morris, and a huge defensive stand down the other end, meant Tauranga Sports stay undefeated, leaving the Mount to again wonder what might have been. Tauranga Sports coach Mike Rogers paid tribute to a beaten Mount side that could easily be undefeated after four rounds had a thing or two gone their way.
"Not taking anything away from the Mount. They put us under a huge amount of pressure that we hadn't gone through so far this season," said Rogers.
"We knew they'd bring that, and we knew pretty much what they'd bring in terms of a game plan.
"It was obviously pretty difficult for us to stop that flow, but we're pretty thrilled to come away with a win, given the circumstances.
"I think our boys showed a lot of ticker in those last twenty minutes to come back. Our theme through the week was brotherhood and they showed that."
In other premier action, Greerton Marist thumped Rangataua 45-7, Te Puke fought off a strong first half from Rotoiti to win 32-9, Whakarewarewa snuck by Opotiki 22-15 and Te Puna beat Paroa 41-12.
Katikati, Rangiuru, Kahukura, Poroporo and Marist St. Michaels ran out winners in division one action.