The Aguias head into the tie on the back of a 2-1 defeat in Russia which left them bottom of their group with just one point from three matches.
Having already succumbed to a 2-0 home defeat against group-leaders Barcelona, another reverse at the Estadio da Luz would all but put paid to their hopes of securing qualification for the knockout stages.
Benfica also lost at home to Chelsea in the last season's quarter-finals and Jesus is eager to avoid setting a new record of three consecutive European losses in front of their own fans.
"This is a decisive game," he told a press conference. "We knew after the defeat to Barcelona that we had to win both games at home, even though we still may be dependent on others.
"There are still nine points up for grabs and if we win, then we can have a chance, so we can only think of a victory and play to that goal."
Jesus added: "Spartak are a quality side and in Moscow we could not impose our rhythm, especially in the first half.
"But at the Estadio da Luz we can be ourselves, we will look to play at our own pace so we can make goals."
Left-back Lorenzo Melgarejo missed Benfica's 3-0 win against Vitoria SC at the weekend because of a knee injury, but trained on Tuesday morning.
However, Pablo Aimar and Carlos Martins are doubtful because of respective thigh problems while fellow midfielder Nemanja Matic is suspended.
Spartak, meanwhile, come into the European tie having thrashed Krylya Sovetov 5-0 last time out.
The Russians will be out to build on a promising performance on their last European away-day, when they lost 3-2 at Barcelona in a match they had been leading before two late goals from Lionel Messi proved decisive.
A home defeat to Celtic, though, has left Spartak with some work to do if Unai Emery's side are to clinch second place.
Czech international defender Marek Suchy is a doubt for the visitors because of a back problem, while Republic of Ireland winger Aiden McGeady remains sidelined by a foot injury.