Ladd and de Haan scored in the third period for the Islanders, who had been outscored 14-1 after the second period in their previous six games.
"I think we just played with the mindset in the third period that it was a 0-0 game," Strome said. "We came out hard, had a lot of scoring chances and it was nice to kind of keep the pressure on rather than sit back on our toes and our heels."
The Sabres (12-13-8), who got 27 saves from Nilsson, have lost three straight games (0-2-1).
"Start to finish, we couldn't generate anything," Sabres captain Brian Gionta said. "We have to do a better job of figuring out what type of a team we want to be. We're the type of team that has to be direct, using our forecheck."
Greiss lost his shutout when Zemgus Girgensons scored with 1:03 left.
"A lot of their shots were from the outside, there weren't really many rebounds," said Greiss, who made 48 saves in a 4-2 win at the Boston Bruins on Tuesday. "It was a great defensive game for our team today."
Kyle Okposo, who was drafted by the Islanders and spent nine seasons with the organization, played his first game here since signing a seven-year contract with the Sabres on July 1. He had two shots on goal and two blocks in 17:58 of ice time.