Matt Duchene got his sixth goal for Colorado. Semyon Varlamov had stopped 20 of 25 shots, and Calvin Pickard had three saves in the third period for the Avs.
Fabbri scored 1:37 into the first on a 2-on-1 break with Dmitrij Jaskin, beating Varlamov to the short side.
Lehtera scored from the slot off a pass from Carl Gunnarsson, getting his first goal 3:35 in.
"The first period today was the best period we played all year," Blues coach Ken Hitchcock said. "Our puck pursuit, our tenacity, our secondary forecheck was excellent. We looked like a team right on the mark.
"Man, we did a lot of things right. You draw up the game plan and that's exactly what you want. I was really happy with how we played in the first period."
After Duchene made it 2-1 by tipping Francois Beauchemin's shot 6:38 into the second, Jaden Schwartz deflected a slap shot by Alexander Steen with 5:06 left in the period and Scottie Upshall buried a back-handed pass from Ryan Reaves about two minutes later.
"It was a great pass," Upshall said. "Our fourth line has been working hard lately and getting some chances. It was nice to chip in."
David Perron scored with 54 seconds left in the second on a shot that deflected off Varlamov's glove and shoulder.
Varlamov was not happy with his performance.
"You saw what happened. I gave up five goals," Varlamov said. "It is my fault. I'll take it."
The Avalanche have totaled three goals in their last four games.
"We've got to look at each other and look at ourselves in the mirror," Beauchemin said. "We can all do more. It's not one, two, three, four guys. It's everybody that's got to step up their game."
NOTES: Blues D Joel Edmundson did not return after getting hit by Rene Bourque along the boards late in the first period with an upper body injury. Hitchcock said after the game it will be "days" for Edmundson to be sidelined. ... Colorado LW Blake Comeau was scratched with a groin injury. ... Avalanche right wing Jarome Iginla skated in his 1,485th NHL game, moving past Rod Brind'Amour for 19th on the NHL career list. Iginla needs three more to tie Wayne Gretzky for 18th.
Colorado: Will play at home against Arizona on Tuesday.
St. Louis: Will play at home against Chicago on Wednesday.