The Bulgarian rider's relentless progress up the steep final climb left the field far behind, giving him victory by an astonishing one minute 26 seconds from second-placed Alexandr Dyachenko (Astana).
Gabrovkski's fellow Bulgarian Danail Andonov Petrov (Caja Rural) was third.
The stage winner's vast gap over the field in the 152km stage earned him a lead of one minute 33 seconds in the general classification.
“We had marked down this stage and as I’m a reasonably good climber, I was the one to go,” he said.
“I decided to try my luck eight or nine kilometres from the finish line as I knew the others would not move before the final three kilometres, which were steeper. I gave it my all, never looked back but I was still very surprised to gain time on the chasers in the climb.”
On Wednesday, the riders will contest a 132km stage between Fethiye and Marmaris.
The Tour of Turkey has eight stages. The race finishes with a stage in Istanbul on Sunday.