Fisichella took an unaccustomed leading role at Spa
The Benetton-Renault team have set their sights on overhauling rivals Jordan and British American Racing after their impressive third-place finish at the Belgian Grand Prix.
Benetton have improved markedly in recent races after a poor start to the season and are now lying seventh in the constructors' championship.
But they are only six points behind BAR and Jordan, who are tied on 16 points.
Benetton's ambitions have been boosted by Giancarlo Fisichella's third place at Spa-Francorchamps on Sunday.
The Italian, who qualified eighth, ran in second place, holding off David Coulthard's McLaren-Mercedes for some time before eventually succumbing.
Now Benetton, who will be renamed after owners Renault next season, are predicting more of the same for the Italian Grand Prix on 16 September.
Benetton technical director Mike Gascoyne said: "If [tyre company] Michelin are competitive, we can do exactly what we did at Spa - qualify in the top 10 and finish in the top six in the race.
"That would put a lot of pressure on BAR and Jordan."
Benetton's improved performance came after the introduction of new aerodynamic parts to the car, which spent the first half of the season close to the back of the grid.
And it follows an impressive display in the German Grand Prix at Hockenheim, where both Fisichella and team-mate Jenson Button finished in the points.
"Our race pace in Hockenheim [another high-speed circuit] was good. OK, everyone fell off in front of us, but we weren't lapped," said Gascoyne.
"If we can finish the season as the fourth quickest car, even if that equates to fifth or sixth in the constructors' championship, that would be a pretty impressive performance from where we were at the start of the season."
Gascoyne, who joined Benetton from Jordan at the end of last year, claims that the team expected their improved performance at Spa.
"We thought we could qualify in the top 10 before we went there - and we revised that to top eight after Friday practice," he said.
"We knew the car was a lot quicker after the big aero changes, so we were fairly confident we would go better."
Gascoyne attributes the team's progress to "hard work on the basics - aerodynamics, lightening everything and so on".
He added that results had been helped enormously by Benetton finally starting "sensible testing" in July.
Work had been delayed by problems with the radical new wide-angle engine that Renault introduced this year, which the car manufacturer always saw as a development season.
"You've got to not let the pressure from the media force you into quick fixes," Gascoyne said.
"We've always said that we will wait for the proper fixes, and we do them, they'll work."