Aho tied the game 1-1 with his first NHL goal at 12:37. After making a pass from behind the goal line, Aho circled the net and finished a rebound from Staal's shot from the slot.
"It was a pretty big goal for me," said Aho, who had six assists through his first 13 games. "I feel so good. It was a good shift for our line and it ends up my first NHL goal."
Aho set up Teravainen for a one-timer from the right hash marks to give Carolina a 2-1 lead at 17:01.
"I thought in the first period, it could have been 5-1," Washington coach Barry Trotz said. "Grubauer, for me in the first period, was the first star. We didn't have a lot of execution, a lot of juice tonight. We were flat, and they didn't let us back in the game."
Carolina took a 3-1 lead at 5:59 of the second period with a power-play goal from Staal. Grubauer stopped a shot from Teravainen, but the rebound came right to Staal, who converted from the left side of the net.
Victor Rask's sixth goal of the season gave the Hurricanes a 4-1 lead at 10:37. After Klas Dahlbeck shot wide, Rask chipped the rebound in before Grubauer could cover the left post.
Aho scored into an empty net with 3:50 left in the third period to make it 5-1.