Anthony Cirelli scored, and Domingue made 17 saves for the Lightning (12-5-1), who have lost consecutive games for the first time this season.
"There's some nights you just have to tip your hat to the other goaltender, and that's what you've got to do tonight," Tampa Bay coach Jon Cooper said. "We did everything we could to try to win that game. I think scoring chances in the game were pretty heavily in our favor, and Hutton kicked them out."
Skinner scored to put Buffalo ahead 1-0 at 17:45 of the first period when he pushed the rebound of a Sam Reinhart shot past Domingue. It was his 13th goal, second in the NHL behind Boston Bruins forward David Pastrnak (16).
Using Victor Hedman as a screen, Okposo made it 2-0 at 5:43 of the second with a shot from the top the right face-off circle through Hedman's legs.
It was the second straight game that the Lightning trailed by two goals in the first half of the game. They fell behind 2-0 to the Ottawa Senators 7:21 into a 6-4 loss Saturday.
"We want to start better," captain Steven Stamkos said. "It's not an easy league to win in, it's not an easy league to score goals in, so when you're spotting teams a goal or two goals early in the game, we know we have it in this room to come back, but you don't want to make that a trend."
The Lightning made a push in the second period, outshooting the Sabres 14-2.
Cirelli beat Hutton on a breakaway to make it 2-1 at 5:58 after Alex Killorn hit him with a lob pass.
"I thought we just gave them a little bit too much room to operate," Okposo said. "We just weren't as sharp; we've got to clean up some stuff. I know we've won the last three games, but we probably only played real good for about a period and a half."
