"It's easier when you get a good start," Backstrom said. "You can play your own game. You don't have to take too many chances."
John Madden and Eric Nystrom also scored, and Martin Havlat had three assists, giving him 13 assists and 22 points in 18 games against Tampa Bay. The Lightning outshot Minnesota 16-6 in the first, and 38-18 overall.
"We had 34 shots in Atlanta [Thursday] and we got one goal, so tonight we capitalized on our chances," Madden said. "As long as we get two points, I'm not really concerned about how many shots be get. I'll take quality over quantity any day."
Martin St. Louis scored for the Lightning, who have lost three in a row and six of seven. Steven Stamkos had an assist, but saw his four-game goal streak end.
"Again, one of those games where we double the shots of the other team and can't get a goal," Stamkos said.
Stamkos, who has 15 goals and 13 points, has a point in 15 of 17 games this season.
Over the last seven games, Tampa Bay has 13 goals.
"We're in a cloud right now," Tampa Bay coach Guy Boucher said. "The opportunities are there. We'll get through it."
Clutterbuck opened the scoring on a flukey power-play goal at 7:16 of the first. His shot from the left circle hit the end boards and rebounded into the crease, where the puck went off the back goalie Dan Ellis' left leg and into the net.
St. Louis tied it at 1 during a power play at 11:31 of the first.
Less than a half-minute after St. Louis skated in alone and had his left circle shot stopped by Backstrom, Madden made it 2-1 from in-close with 7:05 left in the first.
Minnesota, which entered with the NHL's second-best power play, converted its second man-advantage during the first and took a 3-1 lead when Miettinen scored with 29.4 seconds to go.
Tampa Bay entered with the league's second-leading penalty-killing unit and had given just two power-plays goals in 27 opportunities at home this season entering the game.
Nystrom scored an empty-net goal with 48.8 second left in the third. The goal stopped a 23-game goal drought, dating to March 25.
The Wild wound up 2 of 3 on the power play, while Tampa Bay converted one of its three chances.
Tampa Bay C Vincent Lecavalier will have surgery Monday to expedite the healing process for a broken right hand, which will keep him out of action for three to four weeks. He was placed on injured reserve, retroactive to Thursday. ... Wild D Marek Zidlicky returned after missing three games because of a leg injury. ... Lightning LW Simon Gagne (neck), out since Oct. 22, has resumed skating. ... Minnesota D Brent Burns served the first game of a two-game suspension for careless use of his stick. His unintentional hit Friday night broke Florida RW Steve Bernier's orbital bone. ... Tampa Bay RW Steve Downie (back) played after missing the previous three games.