Rooney opened the scoring in Serravalle from the penalty spot in the 13th minute yesterday, leaving him with an identical international record to 1966 World Cup-winner Charlton of 106 caps and 49 goals.
England added to that goal before the interval via a Cristian Brolli own goal, and Ross Barkley's first goal for his country, along with late efforts from substitutes Theo Walcott, who scored twice, and Harry Kane completed a routine win.
England have won all seven games in qualifying Group E and need only draw with the Swiss at Wembley to be sure of finishing in top spot. However, Switzerland make the trip buoyed by their remarkable performance in beating Slovenia 3-2 in Basel.
Slovenia looked set to claim a crucial win thanks to goals either side of half-time from Milivoje Novakovic and captain Bostjan Cesar. But the hosts were given hope when Borussia Moenchengladbach striker Josip Drmic came off the bench to pull a goal back in the 80th minute.
Estonia remain right in contention too after a second-half Konstantin Vassiljev strike secured a 1-0 win at home to Lithuania.