Mark Kastelic and Claude Giroux scored, and Anton Forsberg made 19 saves for Ottawa (14-15-2), which had won four in a row, including 6-3 at the Detroit Red Wings on Saturday.
"We didn't score on our chances, and then they get the same chance and they score," Senators coach D.J. Smith said. "Whether the goalie made a save or bounce, whatever the case may be, those gotta go in the net. We come out, scored, maybe it's a different game, but at the end of the day, we still shot ourselves in the foot with two bad turnovers that end up in our net.
"You're down 3-0 on the road, it's tough to win."
Kaprizov made it 1-0 at 8:19 of the first period on the Wild's second shot of the game. Sam Steel worked the puck loose off the boards over to Zuccarello, who fed Kaprizov in the right circle for a one-timer.
Zuccarello then made it 2-0 at 1:34 of the second period. The rebound of Kaprizov's shot deflected to Steel, who passed to Zuccarello for the finish down low.
Zuccarello has 13 points (six goals, seven assists) during his point streak.
Jared Spurgeon extended the lead 3-0 at 9:27 off a pass from Kaprizov that went through the legs of Travis Hamonic.
Kastelic made it 3-1 at 4:58 of the third period with a deflection of Hamonic's point shot, and Giroux cut it to 3-2 at 18:20 with Forsberg pulled for the extra attacker.