Pavol Demitra, Keith Carney and Todd White also scored for the Wild, who have gone 12-3-2 in their past 17 road games.
Michael Ryan scored for the Sabres, who lost for the second consecutive time at home. Buffalo, the league's top-scoring team, has scored just six goals over the past three games.
Minnesota right wing Marian Gaborik was stopped by Buffalo's Ryan Miller on a penalty shot with 5:27 left in the second period. Gaborik was awarded the shot after being hauled down on a breakaway by Sabres defenceman Nathan Paetsch.
The Wild moved past idle Calgary and into sole possession of second place in the Northwest Division.
Moore, playing in his fourth game since arriving from Pittsburgh in a trade deadline deal, came into the game with just seven goals in his past 99 games. It was his third career multi-goal game.
Harding made just his second start in goal this season, giving Niklas Backstrom a break. Backstrom had appeared in 15 of the past 16 games. Since being called up from AHL Houston in January, Harding has stopped 90 of 92 shots in the four games.
Moore opened the scoring nearly five minutes in when his slap shot from the left circle eluded Miller. The puck appeared to go off Buffalo defenceman Teppo Numminen on its way to the net.
Moore made it 2-0 nearly 10 minutes later with his eighth of the season, taking a pass from Martin Skoula at the right circle before skating in and lifting the puck over Miller's left shoulder.
Demitra pushed Minnesota's lead to 3-0 with his 22nd of the season 3½ minutes into the third, and Carney increased the lead to 4-0 with his second four minutes later. The goal chased Miller, who was replaced by Ty Conklin.
Ryan spoiled Harding's shutout bid with his third goal at 16:01 of the third.
Miller, making his fifth consecutive start, finished with 18 saves, while Conklin made eight saves.
Notes: Buffalo concludes its three-game homestand Saturday against New Jersey, the Eastern Conference's second-best team. It's the first time the Sabres have hosted back-to-back games on consecutive days since Dec. 1998. ... Minnesota C Wes Walz missed his second consecutive game because of an upper-body injury. ... The last time Minnesota played at Buffalo was Oct. 2003. ... It was the final inter-conference game this season for both teams. ... Backstrom was a healthy scratch, with Manny Fernandez serving as the backup goaltender.