Annunen earned the win in relief Tuesday against the Sharks after allowing one goal on 16 shots faced.
Annunen will protect the home goal versus the Golden Knights on Tuesday, Brooks Bratten of the Predators' official site reports.
Annunen will protect the home net against the Kings on Saturday, per Brooks Bratten of the Predators' official site.
Annunen turned aside 35 shots in Thursday's 4-1 win over the Stars.
Annunen stopped 27 of 29 shots in Thursday's 3-0 loss to the Canadiens. The third goal was an empty-netter with 46 seconds left in the third period.
Annunen is expected to start on the road against Montreal on Thursday, per Brooks Bratten of the Predators' official site.
Annunen and a sixth-round pick in the 2025 Draft were dealt from Nashville to Colorado, in exchange for Scott Wedgewood on Saturday.
Annunen stopped 11 of 16 shots in Monday's 8-2 loss to the Lightning.
Annunen will be between the road pipes for Monday's contest against the Lightning.
Annunen turned aside 24 shots in Monday's 3-2 win over the Flyers.