But there the young stars were in Game 3 of the NHL Eastern Conference semifinal against New Jersey earlier this week, holding off the Devils and teaming to score an empty-net goal to secure a 2-0 win and a 2-1 lead in the best-of-seven series.
And they may be there again if the same situation arises in Game 4 on Wednesday night at Scotiabank Place.
The two Ottawa offensive engines have gained the trust of coach Bryan Murray to play at times when defence is the team's top priority.
"Last year, I wouldn't have dared to do that," Murray admitted.
It is appreciated by Heatley and Spezza, who scored the empty-net goal Monday night.
"That's nice to have from a coach," Heatley said after practice on Tuesday. "We showed him that we can play safe and responsible.
"Me and Spez, we're offensive guys. We came into the league as offensive guys and sometimes you get a rap as guys who take too many chances. But this year, we've learned to play a little tighter and he's rewarded us for it."
Even Devils goaltender Martin Brodeur has noticed.
"They're using them in tough situations in their own zone," Brodeur said of Heatley and Spezza. "But they're solid players. It's not like they don't know what's going on."
The line of Heatley, Spezza and captain Daniel Alfredsson hasn't sacrificed any offence, combining for 11 goals in eight playoff games so far, including seven in three games against New Jersey.
But they are also a combined plus-5, thanks to playing smarter defensive hockey.
"By no means are we the best defensive players in the league, but I think we're getting better," added Heatley. "And we still generate offence while playing better in our own end."
Spezza in particular had drawn Murray's ire for giving up turnovers in the neutral zone. The second-year coach said his star centre seemed finally to grasp the message when he returned from a 14-game layoff with a knee injury in January.
The previously struggling Senators had started to pile up wins without him in the lineup.
"He and I have had many discussions," said Murray. "He was frustrated with me and I was frustrated with him.
"But I think he realized that if he played a little harder without the puck, he could really help this team. When he came back from his injury, he got better in critical times of a game and now I feel comfortable putting him out there late in a game."
Spezza said the whole team was playing better defensive hockey because it was going through a spate of injuries at the time. He wanted to show his teammates he could tighten up his game and contribute as well.
"I'm just doing smarter things - not turning the puck over as much and getting back a little harder," the 23-year-old said. "I'm just playing the system like everyone else.
"I don't want to just play 20 minutes-plus when we're losing, I want to play it when we're winning too. It makes you feel good about maturing as a player. And that's how you have to play in the playoffs."
His talks with Murray were two-way conversations, he added, and now they have "a good relationship.
"Bryan's got more confidence in me and I have more confidence in him and his decisions."
It helped both Spezza and Heatley that the veteran Alfredsson was added to their line late in the regular season.
They terrorized the Pittsburgh Penguins in the first round and have kept it going against the patient, tight-checking Devils.
"It takes a bit of pressure off me," said Alfredsson. "I play both ways. I always make sure we have a third man high, but when they work hard, I don't have to worry about defence all the time."
The concern against New Jersey is scoring on Hart Trophy candidate Martin Brodeur, who has been solid against the Senators' high-pressure attack in two games since allowing four goals in the opening period of Game 1.
On Monday night, it took a strange goal from defenceman Tom Preissing after Mike Fisher had clipped Brodeur's skate while passing by the crease to break a 0-0 tie in the third period.
The Senators expect Brodeur and the Devils to be even tougher to beat in Game 4.
"We've got momentum, but we'll have to earn it again," said Alfredsson. "The margins are so small out there.
"We'll have to get our desperation level to where the Devils are because they know that if they go down 3-1, they're probably not going to win the series."
The Devils were also down 1-2 after three games of their first round series against Tampa Bay but came back to beat the Lightning in six games.
"It's a situation we'd rather not be in, but we have to live with it," said Brodeur. "We have to play better.
"But we feel we were able to turn it on when it was time in the other series and we feel we'll be able to do it again. But it's a different task to do it in this building, that's for sure."
Against Pittsburgh, Ottawa took a 2-1 lead and went on to win in five.
New Jersey usually thrives on low-scoring hockey, but the Senators showed they can also play a disciplined game. And goaltender Ray Emery, although he looked iffy on some shots, made 24 saves for the shutout.
"We knew they were a team that played well as a unit," added Brodeur. "What we're seeing is what we expected.
"They're a good hockey team. They have a lot of depth and they're fairly well coached. It's rare to see them running around not knowing what to do in their defensive zone. That makes it tough on us a bit."
Coach Lou Lamoriello said he will consider making lineup changes for Game 4, but would not say what they may be.