Lundqvist stopped all 21 shots he faced in a 1-0 overtime victory over the Red Wings on Sunday.
Hayes (lower body) left Sunday's game against Detroit in the second period and won't return, Justin Tasch of the New York Daily News reports.
Puempel (concussion) has been cleared to play, but won't suit up for Sunday's showdown in Detroit, Steve Zipay of Newsday reports. Additionally, Puempel is no longer listed on injured reserve, per the NHL's official media site.
Staal (concussion) continues to skate on his own, but there is still no timetable for his return.
Lundqvist is expected to start Sunday's game against the Red Wings.
Skjei got the scoring started with his second goal of the year and added an assist as well as a plus-3 rating in Thursday's win over the Leafs.
Hayes notched two assists -- one shorthanded -- and fired six shots on net in Thursday's 5-2 win over the Leafs.
Grabner scored a pair of third-period goals -- one shorthanded, the other an empty-netter -- to seal the deal in a 5-2 win over the Leafs on Thursday.
Lundqvist limited the Maple Leafs to two goals on 25 shots en route to a 5-2 victory Thursday night.
Lundqvist will guard the posts in Thursday's matchup with the Maple Leafs, Justin Tasch of the New York Daily News reports.
Puempel (concussion) will stay back in New York as the team travels to face the Maple Leafs.
Fast will miss 7-to-10 days with an upper-body injury.
Kreider was fined $5,000 for hitting Stars forward Cody Eakin with his helmet while the two fought in Tuesday night's contest.
McDonagh notched an assist for the third consecutive game in Tuesday's 7-6 loss against Dallas.
Vesey skated only 6:18 in Tuesday's loss to Dallas, marking a new season low. He didn't take a shot on goal for the third consecutive game and finished minus-2.
Girardi skated just 17:59 and went minus-1 with a shot and five hits in Tuesday's 7-6 loss to the Stars.
Klein managed an assist, two shots and a plus-2 rating in Tuesday's 7-6 loss against Dallas.
Kreider potted a power-play goal, added an assist and collected seven PIM in Tuesday's 7-6 loss to the Stars.
Stepan scored a pair of goals and added a power-play assist in Tuesday's 7-6 home defeat against Dallas.
Buchnevich scored a goal and assisted on two more in Tuesday's 7-6 loss to Dallas.
Nash handed out a pair of assists and went plus-2 in Tuesday's 7-6 defeat at the hands of the Stars.
Zuccarello handed out a trio of assists (one on the power play) in Tuesday's 7-6 loss to Dallas.
Zibanejad scored a pair of goals and took seven shots in his return from a leg injury Tuesday, but that wasn't enough in a 7-6 loss to the Stars.
Lundqvist was beaten for seven goals on 27 shots before being pulled at the second intermission of Tuesday's 7-6 loss to the Stars -- his third consecutive defeat.
Lundqvist will start between the pipes in Tuesday's home game against the Stars, Brett Cyrgalis of the New York Post reports.