Stuart Skinner made 25 saves for the Oilers (32-21-8), who have lost two straight and six of eight (2-3-3).
"I'm proud of our team with that effort, obviously. Boston's the top team in the NHL for a reason," Edmonton coach Jay Woodcroft said. "They didn't need much in order to score, but when we broke down, they made us pay. We were unable to find the equalizer there in the third period, but I thought there were a lot of positives to take out of that game tonight."
McDavid gave the Oilers a 1-0 lead at 2:17 of the first period. He received a stretch pass from Leon Draisaitl and scored five-hole from the left face-off circle.
Nosek scored 13 second later to tie it 1-1, lifting a shot over Skinner's glove after the puck was redirected in front by Garnet Hathaway along the goal line.
Foligno put the Bruins ahead 2-1 at 15:06, finishing a give-and-go with Charlie Coyle.
"I think we're proud of our process and what's it's allowed us to do and be where we are, but I still think there's room to grow," Foligno said. "I still think there are little areas we can get better in. I'm not trying to sound tacky, it's just the reality of our team. I don't think anyone is satisfied here. I think we're really excited about our group, but I think we all know there is more to do. That's the mindset that's allowed us to have the success we've had."