Ottawa is 3-10-2 since returning from Stockholm.
"Hopefully it's going to give us some confidence," Senators center Derick Brassard said. "We know we can put on a winning streak."
Carey Price made 35 saves in his 10th consecutive start for Montreal since returning from a lower-body injury. The Canadiens (14-15-4) have lost four of their past five games (1-3-1).
They were outshot 38-28 and won 29 percent of the face-offs (19-of-65).
"We need more," Montreal coach Claude Julien said. "We need to create more and we need to create more from the inside. Some nights we have that and tonight we didn't. Until we figure that out and become more consistent, that's what you are going to see."
Pageau, who grew up across the Ottawa River in Gatineau, Quebec, scored at 14:55 of the second period.
Seconds after Senators forward Tom Pyatt got the puck back after a lost in-zone face-off, Pageau found space in the high slot and deflected Karlsson's low wrist shot from the right point past Price for his fourth goal of the season.
His goal would eventually become the game-winner.
"To score that goal was pretty special," Pageau said. "When your goalie doesn't give up one it makes it easier."