Zucker one-timed a pass from Granlund at 4:59 of the third period to give Minnesota a 2-1 lead and extend his goal streak to four games.
Zucker has scored four times during his streak after being held without a goal the previous seven games.
Granlund scored on the power play at 10:09 to make it 3-1. He beat goalie Mike Condon (33 saves) off a pass from defenseman Matt Dumba on a 2-on-1.
"Well, I think we're pretty desperate when you think about it," Wild coach Bruce Boudreau said. "We need the points. I don't think Ottawa does. We are looking at the scoreboard and seeing [the] Colorado [Avalanche] winning [4-2 against the Toronto Maple Leafs] and other teams winning. You know this is a game you should be winning. So, I think we pushed a little harder in the third."
The Wild are on a six-game point streak (4-0-2) and have at least one point in 17 of their past 18 home games (14-1-3).
"We're playing better," Granlund said. "When you're playing better, the results are usually better. Hopefully, we can keep it up and even be better."