Detroit's Jimmy Howard made 23 saves for his 114th victory, tying Dominik Hasek for seventh place on the team's career list.
The Red Wings scored only one goal on six power plays over the first two periods, but they took advantage when Backes' penalty gave them an extra skater for 5 minutes midway through the third period.
Backes was ejected for illegal contact to the head when he used his shoulder to hit Detroit defenseman Kent Huskins high.
"I'm not going to comment on that," Hitchcock said. "It was a big turning point and it turned out being the turning point of the game."
Kevin Shattenkirk, who scored St. Louis' first goal, refused to say the call was the reason the Blues lost.
"There are breaks in the game, and some of them don't go your way," he said. "We've got to do a better job of killing that penalty."
Zetterberg scored at 6:12 and 8:07 of the first period to put Detroit ahead 2-0. The Blues tied it 5 minutes later on goals by Shattenkirk and Matt D'Agostini. Patrik Berglund put the Blues ahead for the first time early in the second period, but they couldn't hold onto the lead.
Zetterberg set up Jonathan Ericsson's tying goal early in the third period and patiently kept the puck before threading a pass through a few Blues on a cross-ice pass to set up Datsyuk's go-ahead goal.
"We have really good starts but after, we relaxed, and they scored some more goals," Datsyuk said. "But Hank had everything under control, so it's OK."
NOTES: Detroit D Ian White, out since Jan. 25 because of a leg laceration, hopes to play Tuesday at home against Calgary. ... St. Louis rookie Vladimir Tarasenko, a 21-year-old forward, extended his point streak to five games. ... Zetterberg, who has a six-game point streak, had two goals and five assists in his previous five games.
Follow Larry Lage on Twitter: http://twitter.com/larrylage