One of Backes' goals never even reached the net. He was awarded a goal with 1:11 left when he broke in on the Jets empty goal and was pulled down by Jacob Trouba.
"That doesn't happen a whole lot," Backes said. "Sometimes when things aren't going perfect for you, you take them any way you can get them. Hopefully, it's the start of a little streak here."
Winnipeg coach Paul Maurice wasn't too pleased that it happened Monday.
"I don't think that game should have gone to 3-1," Maurice said. "I don't think that's an automatic goal. I don't think it's a slash. He goes down, maybe they locked feet. But it's not unimpeded progress. That game should be still 2-1 in my mind.
"But 2-1 is still a deficit for us."
Ryan Miller made 16 saves for the Blues, who are 7-0-1 since he was acquired by trade from Buffalo. St. Louis has won three straight and eight of nine.
Western Conference-leading St. Louis has an NHL-best 101 points. It is the sixth time in franchise history that the Blues have reached 100 points.
Backes has 23 goals this season. Brendan Morrow added a goal, and Jay Bouwmeester had two assists in the Blues' victory.
Montoya thought his team fell into the Blues' trap.
"This is what that team does," Montoya said. "They get up by a goal and they hold the fort."
Blues coach Ken Hitchcock said his team could easily have had a bigger lead.
"We made a game of it because we couldn't pull away in the second period when we had all the scoring chances," Hitchcock said. "We really played well in the second period."
Tarasenko is expected to miss six weeks because of a hand injury sustained Saturday against Nashville. Oshie, whose first child was born earlier Monday, should be back for Wednesday's game at Chicago.
Backes broke a 1-1 tie with a power-play goal at 13:09 of the third period when he swatted in a rebound of Ian Cole's shot.
After a listless first period, St. Louis took a 1-0 lead just 1:44 into the second. After Winnipeg's Devin Setoguchi failed to control a bouncing puck, Derek Roy took it and broke in on left wing. He centered a pass to Morrow on the right side for a shot into the open net.
The Jets took advantage during 4-on-4 play to tie it at 1:55 of the third. Evander Kane skated down left wing with O'Dell on a 2-on-1 break. Kane centered a pass to O'Dell, who faked a shot and then beat Miller with a backhand.
St. Louis is 38-1-5 when scoring first and 30-0-4 when leading after two periods. ... Winnipeg is 8-13-5 against the Central Division. ... Hitchcock moved into sole possession of third place on the team's career victory list with 119.