Dellandrea picked up an assist in Tuesday's 7-6 overtime win over the Sharks.
Dellandrea posted an assist in Saturday's 6-2 win over the Devils.
Dellandrea has played in just seven of the Stars' 23 games since the start of December.
Dellandrea has played in nine of the Stars' last 18 games.
Dellandrea (face) is in Monday's lineup against Columbus, Saad Yousuf of The Athletic reports.
Dellandrea signed a one-year, $900,000 contract with Dallas on Thursday.
Dellandrea scored two goal on three shots and added three hits in Saturday's 4-2 win over the Golden Knights in Game 5.
Dellandrea (illness) will be a game-time call for Thursday's Game 5 against the Kraken, Brian Rea of Bally Sports Southwest reports.
Dellandrea (illness) was not on the ice for the morning skate Tuesday ahead of Game 4 against Seattle, Saad Yousuf of The Athletic reports.
Dellandrea scored a goal in Monday's 6-1 win over the Red Wings.