Rooney scored in the 10th minute, slotting home Glen Johnson's pass for his first England goal since last Sept. 9 against Croatia.
Teenager Xherdan Shaqiri gave Switzerland hope with a long-range goal in the 71st, but England substitute Darren Bent sealed the game in the 88th with a low shot.
Following its 4-1 loss to Germany in the second round of the World Cup, coach Fabio Capello's team opened Euro 2012 qualifying with back-to-back wins. The Three Lions routed Bulgaria 4-0 at Wembley last Friday.
England resumes Group G play at home against Montenegro on Oct. 12, four days after Switzerland travels to the Montenegrins.
Capello insisted on Monday that it was best for Rooney to play to escape the pressure in his personal life following Sunday tabloid stories alleging he cheated on his pregnant wife last year with a prostitute.
England soon mastered a wet field soaked by a downpour during the warmups and scored at the end occupied by its 3,000 traveling fans.
Johnson overlapped, and the right back pulled back a pass that was perfectly dummied by Jermain Defoe for Rooney, arriving late and unmarked, to slot home in front of goal.
It was a 26th international goal for the Manchester United forward, who was then joined on the field by a fifth Manchester City player when Adam Johnson replaced Walcott, who was injured in the scoring move. The Arsenal winger was taken to hospital for scan on a suspected sprained right ankle.