Brock Nelson had a goal and an assist, Anders Lee and Cal Clutterbuck scored, and Lehner made 37 saves for the Islanders (35-18-7), who were coming off a 4-2 loss at the Calgary Flames on Wednesday. New York leads the Washington Capitals by two points for first place in the Metropolitan Division.
"It's a point, but it's sour," Lee said. "We wanted to stop it at one (loss) and we were a couple of minutes from doing that. That's been our M.O. this year, being able to bounce back from losses and bad games, ones we haven't been able to play well in. We're usually able to rebound and get things back on track."
Draisaitl scored on the power play at 5:12 of the first period to give the Oilers a 1-0 lead.
Gagner converted a cross-crease pass from Tobias Rieder at 6:30 to make it 2-0. Edmonton traded forward Ryan Spooner to the Vancouver Canucks for Gagner, who played for the Oilers from 2007-14 after they selected him with the No. 6 pick in the 2007 NHL Draft.
"The important thing is getting the win," Gagner said. "We've been fighting it a little bit, even though we have played some pretty good hockey. A lot of times you can fight through that and get a win and hopefully go on a streak here. That is our focus. This is a huge win for us and will give us some confidence."
Lee made it 2-1 at 12:57, scoring on his own rebound.