Rasmus Ristolainen scored, and Linus Ullmark made 19 saves for the Sabres (0-2-0), who were 0-for-5 on the power play.
"I think the disappointing thing for all of us would be the power plays we were able to get," Buffalo coach Ralph Krueger said. "We had unbelievable discipline again today with no penalties taken, but all those power play opportunities, then the 6-on-5 at the end, coming out empty-handed is certainly the reason we lost this game. I thought the 5-on-5 game was outstanding. We'll take that on any night. Our power play just didn't get the job done today."
Buffalo forward Jeff Skinner said, "You're going to have good games where you don't win and maybe this was one of those for us tonight, but this game is about results. This league is about results. We need to get back at it, keep working and try to get a win the next game."
Jakub Vrana put the Capitals ahead 1-0 at 1:34 of the second period when Wilson sent him in on a break at the blue line.
Ristolainen's shot from the point tied it 1-1, beating a screened Vanecek 31 seconds into the third period.
"There's not much of the 5-on-5 game that we didn't like tonight," Krueger said. "You can take a lot of confidence out of that game, and hopefully the guys, they're able to absorb this pain properly and continue with the process. Really, really good skating, lots of puck pressure, good puck movement, support, all the things we've been trying to get here already in game two. Pleased with the execution."