The Hurricanes (26-22-5), playing the finale of a three-game trip, have sent Brind'Amour (lower body injury) back home for evaluation and lost Staal in a 4-3 win over San Jose on Thursday night.
Staal, Carolina's leader with 22 goals, left the game before the third period. He could have played but it might have hurt his status for this contest, according to Hurricanes coach Paul Maurice.
"The call was that if (Staal) played in the third, he had a chance to make the injury worse," Maurice said. "If he didn't, there was a good chance that he could play on Saturday."
Staal's string of 332 straight games, including playoffs, is in jeopardy. The Hurricanes' highest-paid player is second on the team with 38 points, but was going through a tough stretch in November before facing the Coyotes (24-24-5).
Staal hadn't scored in eight straight games, his worst stretch since he went nine without a goal in 2006-07, but had a hat trick to lead Carolina to a 5-2 win on Nov. 21. He has 14 goals and 11 assists in 33 games since then.
With Brind'Amour missing his first game of the season Thursday, 23-year-old Czech rookie Jakub Petruzalek made his NHL debut and had an assist. Petruzalek was recalled earlier in the day from Carolina's top minor-league affiliate in Albany, where he was second on the River Rats with 34 points in 47 games.
He helped the Hurricanes win for the fifth time in seven games and stay one point behind eighth-place Florida in the Eastern Conference.
Phoenix, trying to avoid falling out of the playoff hunt in the West, is in danger of losing six in a row for the first time since an 0-5-1 stretch in February 2007.
"It's disappointing; got to find a way to win," captain Shane Doan said.
After scoring one goal in its previous three games, Phoenix finally showed some life on offense in a 5-4 loss to Detroit on Wednesday night.
The Coyotes went 1-for-21 on the power play in the first four games following the All-Star break, but went 2-for-4 versus the Red Wings.
Ed Jovanovski and Joakim Lindstrom both had a power-play goal for the Coyotes. Jovanovski, a defenseman, is fifth on the team with 25 points (four goals, 21 assists).
The Coyotes, though, were short-handed on the blue line again, with Derek Morris missing his fourth game with an upper body injury. His status for this contest is uncertain.
Phoenix is 3-0-1 with one tie at home against Carolina since a 5-4 loss on March 6, 1998.