Building off a three-point game in Tuesday's 4-0 win over Philadelphia, Foligno scored for the second straight game at 12:08 of the second to tie it at 3.
The son of former NHL player Mike Foligno, the Senators prospect beat Olaf Kolzig with a nifty backhand for Ottawa's second goal in a span of 1:56. He had a goal and two assists against the Flyers in London, Ontario, on Tuesday.
Heatley put the Senators ahead 4-3 when he scored 4:20 into the third with the Senators on a 5-on-3 advantage. Kelly made it 5-3 at 6:09 after he received Foligno's pass and beat Kolzig with a shot from the slot for Ottawa's fourth straight goal.
Alex Ovechkin scored Washington's fourth goal 15:40 into the third to draw the Capitals within one.
Tom Poti had a goal and an assist as Washington scored two of its first three goals on the power play to build a 3-1 lead 7:34 into the second.
Poti assisted on Capitals captain Chris Clark's power-play goal 16:40 in, and put a slap shot past Martin Gerber for Washington's second with the man advantage
Thomas Fleischman gave Washington a 2-1 lead with 32 seconds left in the first when his centering pass struck Ottawa defenseman Chris Phillips' left leg and sailed past Gerber, who made 52 saves for the shutout Tuesday.
Gerber stopped 15 of 18 shots before he was replaced midway through the second by Brian Elliott, who made 13 saves.
Kolzig played the entire game, stopping 25 shots.
Copyright by STATS LLC and The Associated Press
Arena: Canadian Tire Centre Location: Ottawa, Ontario
Chris Clark (power play) Assist: Tom Poti, Mike Green
Daniel Alfredsson Assist: Jason Spezza
Tomas Fleischmann Assist: Milan Jurcina
Tom Poti (power play) Assist: Mike Green, Viktor Kozlov
Jason Spezza Assist: Christoph Schubert, Wade Redden
Nick Foligno Assist: Antoine Vermette, Christoph Schubert
Dany Heatley (power play) Assist: Daniel Alfredsson, Wade Redden