With Keefe, the Leafs have been ahead 1-0 in five games, and have scored at least three goals in the first period in three games.
"We got off to a good start, (Andersen) made some big saves and we got to roll all four lines during the game", Matthews said.
Jason Spezza also scored for the Maple Leafs, and Frederik Andersen made 26 saves.
David Perron and Ivan Barbashev scored for St. Louis, which has lost two in a row following a four-game winning streak. He allowed four goals on the first eight shots he faced and didn't finish the first period.
"I don't think we look at it that way", Leafs captain John Tavares said on Saturday morning about using the Blues of 2018-19 as a model.
The Leafs have been much sharper while shorthanded, killing off 18 of 20 minor penalties they have taken to go down a man. "We know what we did wrong". They scored four times in the first period, including a three-goal volley in 6:06. "It happens", he said. ". We made a couple mistakes, mistakes that you shouldn't make".
Hyman scored his second goal of the game by converting on a short-handed breakaway for a 3-1 lead.
"We played with confidence a little bit better", Spezza said. The Blues tied it at 1-1 with 7:18 left in the second period on a Zach Hyman goal assisted by Alexander Kerfoot and Cody Ceci. The puck caromed to the side of the net and he was able to lift his shot over Allen.
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Matthews had gone a season-high five games without a goal. He took a flawless pass from Pierre Engvall as they broke in alone on St. Louis goalie Jordan Binnington.
"It's a huge relief", Matthews said. "I don't think that we were overly bad before, but I think that you spend a couple kills together, you start to build confidence and then you start to roll". "It's really important, as we get better in the season and the games get closer, playing with a lead and not letting go is really important".
Perron's redirection of Pietrangelo's right point shot at 2:02 of the third period brought the Blues within 5-2.
"It's got to feel good for him", Keefe said.
"We're not anxious about him".
"He's always been a pretty calm and collected guy", said winger Kasperi Kapanen, one of a number of Leafs who played for Keefe with the AHL's Toronto Marlies. I'm not anxious about him at all. Pierre Engvall had a ideal pass when they came on as a substitute against St. Louis goalkeeper Jordan Binnington.
NOTES: St. Louis LW Zach Sanford left the clinic in the first period with an upper body injury and did not return.