Rooney opened the scoring for Fabio Capello's team as they secured a convincing win against an aggressive Swiss side reduced to 10 men for the last 25 minutes.
Substitutes Adam Johnson and Darren Bent were also on target as England started their Euro 2012 qualifying campaign with six points, seven goals and two fine performances.
Reluctant hero: Wayne Rooney is congratulated by his team-mates
Capello said: 'Rooney scored the goal and it was important for him and us. He played well. He was always the centre of the play and movement. The pressure was really on him but he played really well.
'I told you he'd been OK in training. I had seen that. The players want to play without other things on their minds. They can focus on the game alone. He did that. He was really happy at the end, as were the other players.
'The result was really important. We played the first half really well, fantastic football, and had a lot of chances to score the second goal. We played a little bit lower in the second half, even though we had chances.'
Leading the way: England captain Steven Gerrard applauded Rooney's desire to play
England captain Steven Gerrard also applauded Rooney, who opted to play for his country despite the pressure on his marriage from allegations that he had a relationship with a prostitute. When Rooney scored his 26th England goal in the 10th minute, it was his first for his country in nearly a year.
Gerrard said: 'All the talk before was about Wayne, so it was nice for him to get the early goal and I'm sure that helped his performance.
'He was terrific, like he was on Friday. I'm sure he'll be great for us throughout the qualification games.
'Our first-half performance was perfect, everything the manager asked of us. We got the game plan spot-on. We got a little bit lazy in the second half and they came into the match, but it was never in doubt. People were talking about how good Switzerland are defensively but we tore them apart.'
The wins against Bulgaria and the Swiss have helped to restore pride but Gerrard added: 'We're nowhere near there yet. It's going to take another two years to prove to our supporters and the rest of the world that England are back.
'Two good results do not make you a good team. What makes you a good team is qualifying easily out of the group and going into a big tournament and proving that you can mix it with the best.'
Theo Walcott was taken to hospital after twisting an ankle but X-rays showed no break and he expects to be back in a fortnight. Jermain Defoe also hobbled off with an ankle injury and will have a scan today.
Adam Johnson came on for Walcott and grabbed his second goal in two games. Sunderland striker Bent, who replaced Defoe and scored his first England goal, said: 'It was great to score my first goal. Hopefully, now I'll get many more.'
James Milner collected a second booking and will miss next month's game at home to Montenegro.
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