After their nine-game winning streak was snapped Thursday by Columbus, the Blues erased an early deficit with four consecutive goals before thwarting a late comeback attempt by Toronto.
Drake gave St. Louis a 2-1 lead midway through the first period with his fifth goal of the season and ended the Maple Leafs' hopes with 2:49 remaining to complete his first multi-goal game since November 18, 2000 against the Blues as a member of the Phoenix Coyotes.
Weight continued his torrid pace, tallying twice in the third period to give him seven goals and 19 points in his last 10 games.
"We're deeper than people think offensively because we played such a sound game defensively," Weight said. "We've all bought into this system, that if it's not going in for us, we've got to be good defensively. I think that it has been beneficial. We are going to try to keep doing it."
Fred Brathwaite stopped 18 shots for the Blues, who improved to 6-1-1-1 in the last nine meetings with Toronto.
"It's fun when you're winning," St. Louis right wing Jamal Mayers said. "It's fun to come to the rink. Freddy has been coming up with key saves and playing well for us. There's just a number of guys that are just playing well together. It makes it fun, and that's why we have had a little bit of success here."
Mikael Renberg scored two goals for the Maple Leafs, who have lost three of four.
Mats Sundin staked Toronto to an early lead, slapping a shot from above the left faceoff circle past Brathwaite's stick side at 3:42 for his seventh goal.
Drake put the Blues ahead at 13:14, knocking in a loose puck after a scramble in front, and Mayers cut around defenseman Jyrki Lumme in the left circle before beating Kidd on the short side for the only goal of the second period to make it 3-1.
"We've been getting opportunities over the line," Mayers said. "Hopefully, we can keep it going. There will be nights when they are going to go in for you. We have to keep our frame of mind and work hard."
Just 69 seconds into the third, Weight took a pass from defenseman Mike Van Ryn at the top of the slot and wristed a shot that got past Kidd to give St. Louis a three-goal cushion.
After Renberg halved the deficit for Toronto with his third goal at 11:23, Weight skated down the right wing, cut into the circle and deposited a wrister just inside the left goalpost 3:13 later to mark the fourth time in the last six contests the Blues have netted at least five goals.
"We scored big goals by coming back strong after killing off penalties," St. Louis coach Joel Quenneville said. "We've been playing great in groups and as a team."
Renberg put in the rebound of a shot by defenseman Tomas Kaberle 27 seconds later for his first multi-goal game of the season before Drake put away the game with a power-play tally at 17:11.
Toronto essentially played shorthanded for a full period, committing 10 penalties.
"It's definitely frustrating," Maple Leafs left wing Darcy Tucker said. "We had been up 1-0 and had the opportunity to be 2-0. Then the penalties started. It's tough to play when you have 12 or 13 penalties and keep the momentum of the game going. It was 5-on-4 most of the game. It's hard to play like that."
"When you have penalties, it's hard to win hockey games," Toronto coach Pat Quinn added. "We're going to have to get through this. We have to start thinking about doing something."