Hutchins was diagnosed with Hodgkin's lymphoma in December 2012 and had to endure six months of chemotherapy before being told he was in remission in July.
The 28-year-old has been working towards returning to tennis ever since and spent part of the off season training with great friend Andy Murray in Miami.
Fleming and Hutchins lost in the first round of both their warm-up tournaments and it looked like it would be the same again for much of their 4-6 6-4 6-0 victory over Australian Marinko Matosevic and Pole Michal Przysiezny.
Hutchins played a nervous first game in stifling conditions to drop serve, and that was enough to see the opening set slip away, although they at least gave themselves a chance with two missed break points in the 10th game.
Fleming took a medical timeout to have his left thigh massaged after the ninth game but the British pair made a much better start to the second set.
They could not threaten their opponents' serve, though, and looked in deep trouble when Hutchins trailed 15-40 in the ninth game.
But the Londoner saved both the break points and then put away a volley as they broke to take the set.
Matosevic and Przysiezny never recovered and it took Fleming and Hutchins only 20 minutes to wrap up the deciding set to love before sharing an emotional hug.