New Jersey, however, hasn't won in Dallas in almost nine years.
Kovalchuk and the Devils look to end that drought by extending their winning streak to eight when they visit the Stars on Tuesday night.
New Jersey (25-30-4) is on a torrid 15-1-2 run over its last 18 games, winning seven in a row while holding opponents to eight total goals.
The Devils, searching for their first eight-game win streak since Oct. 29-Nov. 14, 2009, have used that outstanding run to gain significant ground in the Eastern Conference.
They're 10 points behind Carolina for the East's final postseason spot after being as far back as 27 points after losing 2-1 to Philadelphia on Jan. 8.
Kovalchuk has been a major force for New Jersey with 11 goals and nine assists over the last 18 games. The star right wing has seven goals and five assists during a 10-game point streak, matching his career high for a second time and first since Dec. 10-28, 2009.
Kovalchuk kept his streak going Saturday with an assist while Dainius Zubrus scored twice in a 4-1 win over the Hurricanes in the opener of a four-game road trip.
"We played so strong the whole game," said Johan Hedberg, who made 24 saves Saturday. "We didn't give up much."
Although Dallas (31-22-6) has struggled lately, the Devils have lost four in a row at American Airlines Center since last winning there March 10, 2002.
The Devils also fell 4-3 in overtime at home against the Stars on Oct. 8, despite two assists from Kovalchuk.
The Stars, though, have dropped eight of nine with the lone win coming via the shootout, 4-3 against Chicago on Feb. 11. They followed that with four consecutive losses, falling 5-2 at Vancouver on Saturday.
Dallas is tied with Minnesota, Los Angeles and Anaheim for the final two playoff positions in the tightly packed West.
"Guys are feeling the pressure of being in a race and not being at your best," said coach Marc Crawford. "When you go through tough times, you can't just have four or five guys play hard and well."
Brenden Morrow, the team leader with 25 goals, was one of the few Stars praised by Crawford. The Dallas captain has seven goals and two assists over the last 12 games.
Goligoski, a puck-moving defenseman, has nine goals and 22 assists on the season, setting up three goals over the last four games.
Martin Brodeur, who made 24 stops in the most recent meeting with Dallas, has missed six games while recovering from a knee injury. He's served as Hedberg's backup for the last two.
Brodeur is 7-3-1 with a 1.69 goals-against average and three shutouts in his last 11 games against the Stars.
Hedberg has been superb in his place, winning six straight starts with a 1.14 GAA and a shutout.
A member of the Stars during the 2005-06 season, Hedberg has faced his former team once since, making 13 saves in 41:17 of relief in a loss with Atlanta on Nov. 17, 2006.
AccuScore has powered more than 10,000 simulations for every NHL game on ESPN.com, calculating how each team's performance changes in response to game conditions and opponent's abilities. Each game is simulated and the game is replayed a minimum of 10,000 times to generate forecasted winning percentages.