But perhaps most importantly, the Senators played well with their fathers in the stands.
Many of the Senators players' fathers are on this two-game road trip and no doubt approved of their sons' performances.
"You always want to make your dad proud," Foligno said. "Sometimes it's tougher to have your dad yelling at you than your coach."
Kyle Brodziak scored for the Wild and had another goal waved off because of too many men on the ice. The goal would have given Minnesota a 2-1 lead midway through the second period.
Instead, Foligno scored 9 seconds later and the Wild never recovered.
"We were all yelling from the bench that there were too many men on the ice," Senators coach Cory Clouston said. "Lucky for us one of the linesman caught it."
Brodziak said the blunder was his fault.
"I jumped early. It looked like (Koivu) was coming (to the bench) and instead of making sure, I jumped too early and that's why we got the penalty," Brodziak said.
Video replays showed officials made the correct call, giving the Senators a rare stroke of good fortune on the road. Ottawa (14-16-3) had been outscored 24-9 while dropping five of its last six away games before Thursday.
Alfredsson knocked the puck over a sprawling Jose Theodore early in the second to make it 1-1. Alfredsson leads the Senators with 20 points, but has registered only two goals in his last 13 games.
Pierre-Marc Bouchard set up Brodziak for an easy one-timer in front of the net that gave the Wild an early 1-0 lead.
Minnesota (13-13-4) had a chance to extend its lead later in the period, but failed to score during a 41-second, 5-on-3 power play.
"You look back at the game and the missed opportunities," Wild coach Todd Richards said. "Maybe if you can come out of the first at 2-0 or 3-0, but it didn't work out that way. Then in the end, we got what we deserved."
The Wild did not score on three first-period power plays. Both of Ottawa's goals came on power-play opportunities.
"The difference tonight was obviously special teams," Alfredsson said. "We killed some big penalties in the first period and took advantage of our own chances."
Theodore got the start for Minnesota over Niklas Backstrom and made 22 saves. Backstrom was 1-4-1 with a 4.80 goals-against average in his last six games.
Kelly added an empty-net goal late in the third.
Pascal Leclaire stopped 23 shots to help the Senators win for just the third time in their last seven games.
Ottawa, which won its fifth straight over the Wild, has gone 5-9-2 since winning seven of nine games a month ago.
Notes: The Wild honored new Hockey Hall of Fame inductee Dino Ciccarelli with a ceremonial puck drop before the game. Ciccarelli played nine seasons for the Minnesota North Stars. ... Wild C Matt Cullen missed his third game with a groin injury. Cullen helped the Senators reach the playoffs in 2009-10 after joining the team late in the season. ... Senators D Sergei Gonchar recorded his 700th career point with an assist on Foligno's goal. ... Senators D Chris Phillips took a puck to the side of the head and cut his ear in the first period. He had the cut glued and returned to the game.