Alternating streaks with Jaroslav Halak, Elliott turned away all 20 shots for his eighth shutout and St. Louis' franchise-record 14th of the season in the NHL-leading Blues' 4-0 victory over the Phoenix Coyotes on Sunday night.
Elliott and Halak have combined for 14 shutouts to break the team mark of 13 set by Glenn Hall and Jacques Plante in 1968-69, and are the first goalie tandem in NHL history to each have at least six shutouts in one season.
"It's been this way all season," Blues coach Ken Hitchcock said. "One gets hot, cools off and then the other one gets hot. Halak was going good about 2½ weeks and now it's Brian. It's a great situation."
"We didn't get the start we wanted," said Elliott, who improved his season record to 22-9-3. "They were worn out and played the night before. We took advantage of that, scored when we had to score and buried them. We haven't been able to do that in a long time."
The Coyotes remained seventh in the Western Conference with 87 points, one point ahead of Los Angeles, San Jose and Colorado. Phoenix and Colorado have played 77 games, while Los Angeles and San Jose have played 75.
The key to the Blues' success is their style.
"They don't give you much room up the middle," Phoenix forward Lauri Korpikoski said. "The five guys back do a good job of taking you to the outside and let their goalie see everything."
Pietrangelo opened the scoring with his second-period goal with the man advantage.
Backes added his 23rd of the season on a tip in front of Jason LaBarbera at 4:09 of the final period.
The Coyotes had early opportunities on two power plays, but did not capitalize. Their best chance in the opening period came late in the session.
The Coyotes had another power-play opportunity late in the period, but that was negated when Antoine Vermette was called for hooking at 18:57 to create a 4-on-4 situation.
With Vermette still in the penalty box and Phoenix skating short-handed, Pietrangelo scored when his shot beat LaBarbera to the short side 33 seconds into the middle period. The goal was Pietrangelo's second in his last 22 games, and gave the Blues all the scoring they needed.
Last in the league in power-play efficiency, the Coyotes finished 0 for 4 with the man advantage.
"We didn't do enough to win," Phoenix coach Dave Tippett said. "We didn't get the save and they scored with an easy power play to get things going. That's the way the game went."
Phoenix D Derek Morris played in his 1,000th NHL game. The game was the 3,500th in Blues history. ... Bolduc was fined $2,500 for slew-footing Sharks forward Ryane Clowe on March 24. ... LaBarbera made his first start since March 9 at home against Minnesota, and his second start since Feb. 13. ... Phoenix D David Schlemko played his first home game since Jan. 7 against the Islanders.