Coming into the tournament off the back of a poor club season with Lyon, Hegerberg is leading Norway's bid for a first major honour since gold at the Olympics 25 years ago.
The 30-year-old has shown renewed desire as Norway collected a perfect nine points from three Group A matches to set up a clash with the Italians.
Hegerberg got Norway up and running in the opening 2-1 win over hosts Switzerland, netting the equaliser before winning and missing a penalty and then provoking the decisive Julia Stierli own goal.
She was made captain in February and is flanked by vice-skipper and Barcelona star Caroline Graham Hansen.
An honour which came after a turbulent time with the national team, which included a five-year hiatus from international football between 2017 and 2022, provoked by tensions with the Norwegian FA over unequal treatment of women's footballers.
"It's a role that requires experience and the attitude that says we need a good balance between the youngsters and those of us who have been here for a while," said Hegerberg after the Switzerland win.
"We know we have a big role to play on and off the pitch."
The Norwegians were pioneers of modern women's football and the first country to win the World Cup, European Championship and Olympics, but have fallen behind since triumphing at the Sydney Games.
Now managed by Gemma Grainger, Norway failed to get out of the group stage at the last two Euros, and they haven't reached the semi-finals of a summer tournament since reaching the final of Euro 2013.
And they were humiliated 8-0 by England at the last Euros, a tournament that Hegerberg played in after her exile from the international game.
'Relish the moment'
Now Hegerberg has the chance to lead Norway back into the latter stages of a European Championship, with holders England or Scandinavian rivals Sweden.
"We took nine points in the group stage and are playing in the quarter-finals. It's a big moment for us. Everyone has contributed, and we want to ride the crest of that wave," Hegerberg told reporters on Tuesday.
"To get a top-four position at the Euros would be unique. It's a very important game, with a lot at stake, and we want to relish the moment. The way we have acquitted ourselves as a team has been exceptional."
Standing in Norway's way are Italy, who came through a tough Group B, which was won by world champions Spain.
Italy, a traditional powerhouse of the men's game, have impressed in Switzerland under Andrea Soncin, although they have struggled for goals.
"They're a good team and they've developed their women's game there a lot in the last few years," added Hegerberg.
"It'll be very cool to play such an important football nation."