The Ducks' attempts to get any closer were thwarted midway through the third when Minnesota defenseman Jonas Brodin beat Gibson glove side from the left wing.
Granlund made it 5-1 with just under four minutes left when he backhanded in a rebound.
"We gained a little bit of momentum with how we've been playing, and we knew it was going to be a game that we needed to play tight," Cogliano said. "We needed to earn it. That's how that team plays, and that's how they've always been. That just shows we weren't willing to do anything to win the game. The score was indicative of that."
Added Ducks coach Randy Carlyle, "We got a little bit more physical at the end of the second period, the last five or six minutes. We thought we'd be able to carry that out into the third and give ourselves a chance. As far as our execution and emotional level, we looked spent. We didn't have any legs underneath us. Those are the questions you're always going to ask yourself."
Anaheim has the weekend before taking on Western Conference frontrunner Nashville on Monday, winners of four in a row.
"It's very frustrating," Getzlaf said. "We're trying to build. Every day you try to be positive. You try to do things properly. For whatever reason tonight, we didn't have it."