Nelson made it 3-0 at 7:56 with a one-timer from the right face-off circle after a turnover by Red Wings defenseman Mike Green behind the Detroit net.
Howard was pulled after Nelson's goal. He is 2-16-1 with a 4.26 goals-against average and .876 save percentage in 19 games this season.
"We haven't been good enough for him," Larkin said.
Filip Hronek scored from the left point to make it 3-1 at 11:45.
Anders Lee gave the Islanders a 4-1 lead at 18:30. Eberle had an assist for his 500th NHL point.
New York hadn't scored four goals in a period since a 6-3 win against the Ottawa Senators on Dec. 28, 2018.
"We were able to capitalize early," Bailey said. "I think that was probably the key for us; we wanted to come out with a good start. Coming off a back-to-back, you want to come out hot, and we were able to put a few past them early and kind of ride that."
Nelson scored his second of the game at 1:59 of the second period on a breakaway after leaving the penalty box to make it 5-1.
Noah Dobson scored his first NHL goal to give the Islanders a 6-1 lead 41 seconds later when his shot deflected off defenseman Alex Biega at 2:40.
"Obviously, it wasn't how you drew it up, but we'll take it for sure," said Dobson, who turned 20 on Jan. 7 and was playing his 18th NHL game.