They'll both likely need to contribute on Tuesday night to capture a victory against the San Jose Sharks, whose offense looks impressive.
New York (1-1-0) continued its nine-game season-opening trip during Madison Square Garden's renovations with a 3-1 win at Los Angeles on Monday. Richards provided his first two goals of the season.
Richards had just 11 goals over 46 contests and one point in 10 postseason games last year. The also oft-maligned Rick Nash - who tallied one goal in 12 postseason contests - assisted on both of Richards' scores.
Callahan, who didn't record a shot on goal in 11:16 of ice time in his return from offseason shoulder surgery, left the game in the second period after cutting his mouth during a collision, but later returned.
Ryan McDonagh was credited with the team's third goal 4:39 into the third period after merely trying to clear the puck. Kings goalie Jonathan Quick attempted to play it after skating out of the crease, but accidentally deflected the puck in.
"I really liked the way we responded after they scored,'' coach Alain Vigneault said of his first victory with his new club. "We came right back at them and we kept pushing the pace. Obviously, we got a little bit lucky on the third goal, but part of this game. You need a little bit of luck, and we got it there.''
As coach of Vancouver from 2006-07 to 2012-13, Vigneault was 11-12-4 against San Jose.
Richards has 21 points in 25 career games against the Sharks.
Callahan notched two goals and an assist in New York's last meeting with the Sharks, a 5-2 home win Oct. 31, 2011. He has five goals and two assists in five career games versus San Jose.
The Sharks (2-0-0) are coming off 4-1 home wins over Phoenix and Vancouver. Rookie center Tomas Hertl - the 17th overall pick in the 2012 draft - scored his first two career goals in the first period Saturday against the Coyotes, one of which came on the power play.
"I think it's great, you can see how he's having fun with it and he's smiling so much," said Patrick Marleau, who accounted for the other power-play goal as San Jose capitalized on two of four chances. "He brings a lot of energy to us and it's fun to see."
San Jose's 51 shots marked the fourth-highest total in franchise history. The Sharks recorded 35 shots in their opener against the Canucks.
Their 31.8 shots per game last year was the league's fourth-highest average
"When you put up 50 shots you get rewarded," said Marc-Edouard Vlasic, who assisted on two goals.
Joe Thornton has tallied 31 points in 30 career games against the Rangers.
The Sharks are just 3-10-1 with two ties all-time at home versus New York.