The pair are likely to start for England against the Azzurri in the Group D opener, with the Manchester United forward bagging a goal in the 2-2 draw with Ecuador.
Sturridge started but failed to score in both of the Three Lions' warm-up matches, but the former Chelsea talisman believes that both players can be key to success against his native side in Brazil.
"Italy has to be able to stop two strong players like Sturridge and Rooney", he told Gazzetta dello Sport.
Zola also believes that Cesare Prandelli's strikers must up their game against Roy Hodgson's side, and believes that the England defence can stand up to the rigours of fast-paced tournament football better than in previous years.
"Italy has more expert players, England has younger players and two magnetic players like Gerrard and Lampard.
"In my opinion Balotelli and Cassano could create some problems to the England defence, but unlike the past, the England defenders are less slow now. Italy and England in general are similar squads, with some certainty and more variables."