Cole scored two goals in the second period when Dallas snapped a tie, and the Stars went on to beat the Predators 4-1 on Friday night.
The Predators (16-18-4) are 1-4-1 since defeating Dallas at home on Dec. 12 and winless in their last five games. They have allowed 21 goals in those games.
"We had a couple of really great scoring chances prior to that," Cole said. "I felt we were creating opportunities.
"Everyone upped their intensity. We got the two quick ones."
Nashville tied it on Kevin Klein's first goal this season at 7:14 of the second. The defenseman skated down the slot and knocked Colin Wilson's centering pass from low in the left circle past goalie Kari Lehtonen at 7:14.
Just 24 seconds later, Cole sent a drive from the right circle into the near corner of the net for a 2-1 lead. Rich Peverley's backhanded pass from the goal line set up Cole.
"We could have been talking about a missed penalty shot, and 3-on-1s and 2-on-1s," Stars coach Lindy Ruff said. "To answer right away was important."
On his second goal, Cole skated in hard at Hutton, then stopped abruptly. The goalie spread-eagled across the net, but Cole fitted the puck between Hutton's left skate and the right post.
"That first shift after a goal is critical," Nashville coach Barry Trotz said. "You want to get it in and get some zone time so you can keep some momentum on the other team. We didn't do that.
"We were in pretty good defensive position on that. It was a seeing-eye puck and that's the way it's been going for us."
Ryan Garbutt tipped in a shot at 4:09 of the third for Dallas' final goal.
Lehtonen made 33 saves. Over the last four games, he has allowed only six goals on 132 shots, a .954 save percentage.
Hutton stopped 30 shots for Nashville, which had changed goalies in its three previous games.
Benn beat Hutton after skating behind the net. Hutton was late getting across, seemingly more concerned with Tyler Seguin on the left side.
"It was definitely a tough way to start," Hutton said. "I tried to battle, but giving up four is not good enough on any night."
Dallas had a chance for a two-goal lead at 16:35 of the first period. Roussel was awarded a penalty shot when he was pulled down after taking a pass at the blue line and splitting two defenders.
It was Roussel's second penalty shot this season. He scored the winning goal in a 4-3 victory at Chicago on Dec. 3.
Nashville outshot the Stars 9-7 in the first, but Dallas also missed seven shots to the Predators' three.
"We stayed a little bit more disciplined," Benn said.
The line of Benn, Seguin and Valeri Nichushkin has totaled 12 goals in the last six games.. Dallas' Alex Chiasson missed his second consecutive game because of the flu.. The Stars removed Aaron Rome (lower-body injury) from the injured list, but placed defenseman Sergei Gonchar (concussion) on the list.. Nashville rookie defenseman Seth Jones, 19, made his first NHL appearance in his hometown. He played for the Bantam Major Dallas Stars while his father, Popeye Jones, was an assistant coach for the NBA's Dallas Mavericks.