Meszaros and Kelly scored 1:08 apart before seven minutes elapsed. Neil made it 3-0 with his sixth goal on a power play at 14:06, and Daniel Alfredsson scored his sixth goal 7:56 into the second to put the Senators up by four.
Minnesota held a 37-16 margin in shots over the final two periods -- and 45-33 overall -- after being outshot 17-8 in the first.
"We were fortunate enough to get a lead," said Emery, who stopped 34 of 37 shots over the final two periods. "I think we kind of woke them up with a big first period. They definitely came hard. We played hard as well, and some of those games you've just got to hang on and use that lead to your advantage, and that's what we did."
"We got that lead and we kind of just sat back, and they took over and outplayed us for that part of the game," Fisher said. "We've got to make sure we play a little bit smarter when we've got a lead."
The Senators, who led the Eastern Conference last season with 113 points, are 4-6 at home this season and 9-11-1 overall.
"The bottom line is we weren't sharp when they dropped the puck," Rolston said. "They got three quick goals on us and then we were fighting back all night. I thought we played well after that, but too little, too late."
Mikko Koivu scored a short-handed goal with 13 seconds remaining to cut the Wild's deficit to 5-3.
The Wild have lost seven of 10 since a 9-1 start.
Emery, who made 16 saves in the second when Ottawa was outshot 17-7, caught a break early in the third on Koivu's slap shot from just inside the blue line. The Senators goalie got his glove on the puck, which was headed over the net but instead struck the crossbar.
Rolston beat Emery with a backhand 10:46 into the third on his penalty shot, awarded when Fisher closed his hand on the puck in the crease after he stopped the Wild captain's backhand on the goal line with his left skate.
Antoine Vermette extended his point streak to five games with an assist on Alfredsson's goal, and 12 players recorded points on Ottawa's first four goals.
Neil scored on Ottawa's first power-play opportunity against the Wild's top-ranked, penalty-killing unit.
Alfredsson made it 4-0 at 7:56 of the second.
Dupuis got his third goal -- his second on the power play -- at 9:08 to draw Minnesota to within 4-1.
Schaefer scored with 1:29 remaining to make it 5-2.
- Rolston beat Vancouver G Roberto Luongo with a slap shot on his other penalty shot attempt on Nov. 2. He is 2-for-4 in shootout attempts this season, and 5-for-11 overall.
- Ottawa had a season-high, three-game winning streak from Oct. 21-26.
- Heatley remained in the game after he crashed headfirst into the crossbar early in the first. The Senators' leading goal scorer lost control as he fell to his knees while Fernandez stopped him on a breakaway.