The loss extended the Maple Leafs' losing streak to six games.
The first of Backes' goals put the Blues ahead 2-1 with 32.3 seconds left in the first period. Backes took advantage of a turnover by Maple Leafs captain Dion Phaneuf and raced into the zone before beating goalie Jonathan Bernier between the legs on the power play.
Backes made it 3-1 at 7:32 of the third period when he beat Bernier with a wrist shot on a breakaway. Blues defenseman Alex Pietrangelo connected with Backes and sprung him free.
Backes scored an empty-net goal with 1:07 to play to complete the hat trick, the second of his career.
"Guys were teasing me that the empty-netter was five-hole too," Backes said. "It's just one of [those] things, I looked up and he was challenging. When he's challenging out on his angle there, it's tough to find ways around him. He's taking away a lot of the net. Try to find a little slice of air between his legs and I was fortunate enough to do that."
Backes has 27 goals this season, four shy of his career-high of 31 set in 2008-09 and matched in 2010-11.
"I think he doesn't give himself enough credit for how good of a 200-foot player he is," Blues coach Ken Hitchcock said. "I think that's one of the things that has really evolved in his game now. He's a really good 200-foot player. He's not just a checker, he's a guy that can play in both ends of the rink. He's very good offensively. He's underrated offensively, and I think people are starting to see that."
Bernier made 44 saves in his first start since March 13 against the Los Angeles Kings. He missed the past five games, all losses started by James Reimer, with a strained groin.
Toronto (36-30-8) is one of four teams with 80 points seeking two wild-card Stanley Cup Playoff spots from the Eastern Conference.
"If we're missing motivation, at this time of the year everyone should have some," Bernier said. "Obviously we knew it was not going to be easy. That's a good team out there; they're first and they showed it tonight."
Ryan Miller made 21 saves for St. Louis (49-16-7), which leads the overall NHL standings with 105 points.
"We hemmed them in for most of the game, and then when they got loose at the end, it was a little bit of a track meet," Hitchcock said. "We did what we had to do. … It was a 5-3 game where I think we could've scored 10 goals tonight. We had so many scoring opportunities, and I thought for the most part, until we got careless and started to get fancy around the net instead of burying it, that we were really playing one of our top games."
Joffrey Lupul gave the Maple Leafs a 1-0 lead at 11:30 of the first period with a power-play goal. Lupul batted a loose puck past Miller after Nazem Kadri knocked the puck out of the air to him. With Miller sprawled trying to find the puck, Lupul fired it underneath Blues defenseman Roman Polak for his 21st goal of the season.
The Blues made it 1-1 with 4:05 remaining in the first period when T.J. Oshie scored his 18th goal of the season. Oshie dove on the ice to poke in a loose puck after a Polak shot got between Bernier's legs. The play was reviewed to see if Steen hit the puck with a high stick but it was ruled he did not.
"I'm not sure how many shots they had in the first period, but it felt like we were doing a pretty good job keeping the momentum on our side and to come back after that one," Oshie said. "I think everyone shook it off pretty quickly there and responded well."
Blues forward Alex Steen made it 4-1 with 2:25 left in the second period when he scored his 31st goal of the season. Steen fired a backhand from the slot that beat Bernier up high.
Maple Leafs defenseman Carl Gunnarsson made it 4-2 4:39 into the third period with his third goal of the season. He sent a slap shot from the high slot through traffic that beat Miller five-hole.
"It's tough being down two, three, four goals, whatever it might be, especially against teams like this, it's tough," Gunnarsson said. "It's not the way we want to do it. It's something we've got to change here. If we play like we did in the third period for 60 minutes, I don't think there are a lot of teams that can beat us."
Toronto forward James van Riemsdyk made it 4-3 when he scored his 28th goal of the season. Van Riemsdyk took a pass from Phil Kessel from behind the net and fired a wrist shot past Miller with 4:06 left in the third period.
"Would've liked to get a hold of those pucks in the third, but that's the way it worked out," Miller said. "I thought Kessel was going to take it around the net and he kind of gets it right back, and the other one I still don't know how that kind of found its way in, so I'm looking to kind of clean my game up."
With the loss, a win by the Columbus Blue Jackets and a shootout loss by the Washington Capitals on Tuesday, the Maple Leafs are tied with the Blue Jackets, Capitals and Detroit Red Wings. All have 80 points, but the other three teams hold tiebreakers against Toronto.
"The whole year we've thought we were a playoff team, and we still believe that now," Lupul said. "It's a matter of just going out there and doing it, I think. Today we came out tentative, and it could be that fear of it slipping away a little bit, but realistically we're still right there with these other teams. There's reason for concern, but it's not completely time to panic. We're still right there."
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