Martin finished ahead of Giovanni Visconti (Bahrain-Merida) and Mattia Cattaneo ((Androni-Sidermec-Bottecchia) at the end of the 165.1km stage from Lajatico to Volterra.
That same trio topped the general classification on a stage which featured a demanding mountain top finish that dropped previous race leader and stage one winner Steve Cummings (Dimension Data) out of contention.
Martin made his move on the second ascent of the eight kilometre long Volterra after the early break had been reeled in. He bridged to Visconti who had broken away earlier, before riding away solo to the finish.
"Yesterday I was disappointed with not being with the first four and I thought the overall ranking was lost," Martin said. "Ultimately that turned out to be profitable because I could benefit from more freedom.
"The team brought me well in the run-up to the final climb, where [Enrico] Gasparotto (Bahrain-Merida) accelerated at the foot. I followed him with four riders, but the climb was ridden tactically because it was not a very steep climb.
"When a group returned with [Marco] Minnaard I immediately accelerated, so Visconti and I were in front. At one point, he did not want to take over and then I decided to attack again. The last two kilometres I went solo. I had a nice gap and managed to keep it."