Dancevic has been on some of the best form of his injury-plagued career, winning last week's Dallas Challenger event and starting in Florida with an opening victory against Jeremy Chardy of France after qualifying.
Ranked 132nd worldwide, Dancevic had won his last nine matches going into the match against Fish, including preliminary rounds at Key Biscayne.
But after a promising start, the 30-year-old went down to Fish for the third time in his career.
Dancevic lost serve in the eighth game of the opening set as the experienced Fish pulled away to a 5-3 lead before closing out the set.
In the second, the Canadian earned the early break for 2-0, but was unable to maintain the gap as Fish broke in the fifth game to get back in contention 2-3
In the second-set tiebreaker, the American earned a 6-1 lead from Dancevic's forehand long over the baseline, with Fish taking victory on the first of his five match points.
In doubles, Toronto's Daniel Nestor and partner Max Mirnyi of Belarus, the second seeds, won their first-round match over American Eric Butorac and Bruno Soares of Brazil 6-3, 7-6 (7-4).
The Nestor-Mirnyi team moved on to a second-round contest with Austrian Olivier Marach and Alexander Peya,