The Marlins have lost nine consecutive games, having won just five times in the month of May.
Miami scored on a passed ball in the first inning and that was the only run for either team until Joyce launched his ninth home run of the year.
Alex Colome (1-0) picked up the win in his major league debut. Colome was called up from Class AAA Durham this week and originally had been scheduled to pitch out of the bullpen.
He was given the start, however, when Alex Cobb was unable to take his turn in the rotation. Colome allowed a run on five hits with seven strikeouts in 5 2/3 innings.
Ricky Nolasco (3-6) suffered the loss, surrendering three runs on four hits in 6 2/3.