David Perron and Ivan Barbashev scored a goal for St. Louis, who lost two straight seasons following a series of four wins.
The Blues would continue to give up goals without answer for the rest of the first period.
The 25-year-old has lined up alongside Auston Matthews and William Nylander for the majority of the year, recording 16 points in 30 games. He broke a 1-1 tie with a wrist shot from the left wing at 6:51 in the opening period.
Matthews, the # 1 NHL Draft 2016 runner-up, scored only one goal in seven career games against the Blues.
Second Period_6, Toronto, Matthews 18 (Marner), 9:29 (pp). Matthews had expressed displeasure with his team's effort in a 6-1 loss Tuesday at Philadelphia, saying "We just kind of folded, kind of just quit".
Not on this night.More news: Naval Base Shooting Looks Like 'Terrorism,' President Trump's National Security Adviser Says
The Maple Leafs led 4-1 after the first period, scoring three times on their first four shots.
Sheldon Keefe figured his most risky forward was on the cusp of creating some damage.
"It's got to feel good for him". "He's pretty shifty. I think him and Willie have a good relationship, so hopefully we can mesh well and create some offence".
Hyman scored his second goal in the match as he converted to a short-handed breakaway with a 3-1 lead.
St. Louis: face the Sabers in Buffalo on Tuesday. "Structure is big for (Keefe), but at the same time, he lets the boys play, which is big for this team with all the skill that we have". "It's really important. As we progress in the season, and games become tighter, playing with a lead and not letting up is really important".
Goalies_Toronto, Andersen 14-7-3 (28 shots-26 saves).More news: Miss Myanmar Is The First Openly Gay Contestant At Miss Universe
"We played a little better with confidence", said Andersen. Binnington has lost back-to-back games in the regular season for the first time.
"I did not think we had come out that badly, but we made some mistakes that went into our net", said St. Louis coach Craig Berube.
"It just doesn't happen overnight", he said.
Notes: St. Louis LW Zach Sanford left in the first period with an upper-body injury and did not return.
Sheldon Keefe's tenure as head coach of the Toronto Maple Leafs couldn't have started any better. St. Louis is 5-2 in its last seven games versus the Eastern Conference.
Putting him on long term injured reserve does open up salary space to recall hot Marlie winger Pontus Aberg, who has 24 points in 22 games, and bring back winger Nic Petan and defenceman Martin Marincin, both demoted when Mitch Marner ended his stint on IR Wednesday morning. Toronto is 4-9 in its last 13 road games.More news: Elizabeth Warren, Buttigieg campaign bicker over tax returns, fundraisers