Kyle Turris, Derick Brassard, Alexandre Burrows and Tom Pyatt scored, and Craig Anderson made 41 saves for the Senators (3-1-3), who have not won at home (0-1-3).
Hischier put the Devils ahead 1-0 at 2:30 of the first period when he took a pass from Drew Stafford from behind the net and lifted a shot past Anderson. After Turris tied the game 1-1 on the power play at 2:57, Hischier scored his second at 4:21. After jamming in the puck at the left post, the goal was upheld after it was challenged by the Senators for goaltender interference.
Brassard (at 5:07) and Burrows (at 7:15) scored 2:08 apart in the second period to give Ottawa a 3-2 lead. The goal was Burrows' 200th in the NHL. Pyatt made it 4-2 at 15:49 of the second period.
The Senators also could not hold a two-goal, third-period lead in a 5-4 shootout loss to the Washington Capitals on Oct. 5.
"Usually we close these really well," Ottawa coach Guy Boucher said. "Both times it's the same reason. We turned the puck over. Puck management from our defensive zone and neutral zone cost us in the end. This is the stuff we've got to clean up. At the beginning of the year, it happens. We've just got to clean it up for the next games."