The Devils (24-12-8) ended a five-game losing streak (0-4-1) against the Capitals (28-14-4), including two losses this season by a combined 10-4. New Jersey moved within four points of first-place Washington in the Metropolitan Division with two games in hand.
Hall picked up a loose puck along the right-wing boards and scored the 29th game-winning goal of his NHL career, his seventh with the Devils. Hall also had an assist to extend his point streak to six games (five goals, six assists).
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"In overtime, we're instructed to strike and create turnovers at the start of your shift since we're rested and 20 seconds in we're trying to create a turnover, trying to force pressure," Hall said. "I saw T.J. Oshie back there and he's a forward and I knew he would play the puck aggressively so I was able to chip it past him.
"On the breakaway, I just had to get it up and get the goalie moving a bit, open up that glove side."
Drew Stafford, Andy Greene and Miles Wood scored, Sami Vatanen had three assists, and Keith Kinkaid made 16 saves for the Devils. Kinkaid won his second straight start; the backup made 25 saves in a 4-1 win at the New York Islanders on Tuesday.