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 both players can be key to success against his native side in Brazil.
"Italy has to be able to stop two stronger 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 defense can stand up to the rigors of fast-paced tournament football better than in previous years.
"Italy has more expert players, England has younger player and two magnetic players like Gerrard and Lampard," he said. "In my opinion [Mario] Balotelli and [Antonio] Cassano could create some problems for England defenders, but unlike the past England defenders are less slow. Italy and England in general are similar squad with some certainty and more variables."