Stillman and Chad LaRose scored, Ray Whitney tacked on an empty-net goal and the Hurricanes beat the Vancouver Canucks 3-1 on Monday night to snap a two-game losing streak.
"The biggest thing is to push to score goals," Stillman said. "We've got to learn how to close teams out, and if you're up by two, to get the third goal."
Cam Ward stopped 19 shots and improved to 5-0 in regulation, Rod Brind'Amour had two assists and Whitney added a helper for the Southeast Division-leading Hurricanes.
Carolina held a 31-20 shots advantage and dealt Vancouver its first road loss of the season and first loss in four visits to the RBC Center.
Injury-depleted Carolina - which was without three key forwards - rediscovered a measure of confidence after a rough weekend trip to Pennsylvania when the Hurricanes blew late leads and lost in the shootout to Pittsburgh and in overtime to Philadelphia.
Those defeats closed a season-long six-game road swing in which they finished 3-1-2 and picked up eight points in the standings.
"Coming back home, you always have concerns about trying to be too cute or your thought process going into the game," Carolina coach Peter Laviolette said. "I thought we were very sharp in both areas tonight."
Brendan Morrison made it a one-goal game by scoring with 6:41 remaining, and Roberto Luongo stopped 28 shots for the Canucks. The reigning Northwest Division champions have lost three of four.
"We won lots of games last year. We were not pleased with our effort, but we were finding ways to win," Luongo said. "I think that's what's missing right now. We're not finding ways to win on a consistent basis."
Stillman put the Hurricanes up 1-0 early in the second period with his third goal of the season, all on the power play. He took a pass from Whitney behind the right circle and one-timed the puck just beneath Luongo's blocker.
The Hurricanes - who last season ranked near the bottom of the NHL with the man advantage - entered third-best in the league in that category, converting on nearly 26 per cent of their chances. They've scored at least one power-play goal in every game but one - a 2-0 loss at Washington on Oct. 6.
"It's important for a power play to continue to score," Stillman said. "One a game, two a game, will allow us to win a lot of hockey games."
Whitney's empty-netter in the final seconds came on the power play and was Carolina's league-best 13th goal with the man advantage.
It came after Morrison had cut the margin to 2-1 by corralling an attempted wraparound from Brad Isbister near the goal mouth and hammering it past Ward's glove side.
Carolina put Luongo to the test early, outshooting Vancouver 16-6 during a scoreless first period and at one point in the second held a 20-6 advantage in shots. That fell in line with their play of late, entering with just eight goals in three games despite averaging 38 shots.
"If you take away the shots after the first 11 minutes, the shots and the chances were about the same," Vancouver coach Alain Vigneault said.
Notes: Vancouver C Trevor Linden was a healthy scratch, and remains one assist shy of matching the team record of 411. ... RW Justin Williams' five-game points streak ended for Carolina. ... Erik Cole (foot) missed his second straight game for Carolina, which dressed only 12 forwards. ... North Carolina State women's basketball coach Kay Yow dropped the ceremonial opening puck as part of the NHL's monthlong "Hockey Fights Cancer" awareness night. The Hall of Fame coach has breast cancer.