Hendricks skated in on Islanders goaltender Evgeni Nabokov, executed a fake to the left, and then switched to a backhander and fired it into an empty net for the Caps, who had trailed 4-1 midway through the second period.
Alex Ovechkin scored twice, including the equalizer with 10 minutes left in regulation, and Keith Aucoin added three assists as Washington claimed its fourth straight win.
Michal Neuvirth made 26 saves for the Caps, who established a four-point lead over Buffalo for the eighth and final playoff spot in the Eastern Conference.
The Islanders got a pair of goals and an assist from John Tavares but let the lead get away and dropped their fourth straight.
Travis Hamonic added a goal and two assists and Nabokov ended with 24 saves for New York.