Anaheim made it 3-2 at 11:46 when Terry laid out for the rebound of a Trevor Zegras shot and made a one-handed backhand swipe into an open net.
"I'm proud of battling back, but on the second night of a back-to-back, especially against the caliber of a team like that, you can't be spotting two goals," Terry said. "We knew we were going to have to play a near-perfect game to play with that team and not make many mistakes."
Staal has scored 13 goals in 71 games, including five in the past three games.
"He's our leader, he brings it every single night," Hurricanes defenseman Jaccob Slavin said. "He cares about the game of hockey and he cares about the guys in the locker room. I look up to him as a player and a person, so when you see guys get rewarded like that, it's special."
NOTES: Ryan Getzlaf was minus-3 with one shot on goal and one blocked shot in 16:51 of ice time after missing five games with a lower-body injury. … Staal's three-goal game established the longest span between regular-season hat tricks in NHL history at 4,898 days. His most recent hat trick came as a member of the Pittsburgh Penguins in a 7-6 win against the Detroit Red Wings on Nov. 11, 2008. … Brind'Amour earned his 167th coaching win, tying Peter Laviolette (2003-08) for second in Hurricanes/Hartford Whalers history. Paul Maurice has 384 (1995-03; 2008-11).