The 19-year-old pounced after just two minutes to stab home Jermain Pennant's dangerous low cross from the right wing, and was generally impressive up against a solid and well-organised Swiss defence before being replaced by midfielder Scott Parker in the 65th minute as manager David Platt attempted to hold his side's lead.
However, the evening was soured somewhat by the performance of Hungarian referee Attila Hanacsek, who produced a number of questionable - and at times bizarre - decisions and almost spoilt the game by constantly penalising players for seemingly fair challenges.
Sean Davis, David Prutton and goalkeeper Paul Robinson were all booked for petty, while several Swiss players escaped punishment for more serious crimes.
England doubled their lead in the 53rd minute, when David Dunn's free-kick was deflected into six yard box, where Defoe's strike partner Peter Crouch was waiting to poke home with the outside of his foot.
The hosts pulled a goal back four minutes later, when Alexander Frei's free-kick from 25 yards out deflected off wall and spun into the far corner of the net past the despairing dive of Robinson.
The Leeds keeper had to be at his best to deny Switzerland an equaliser as they threw everything forward in the closing moments, but England managed to hold on and were further boosted by the news that Italy had drawn 1-1 against Portugal in the other group A game.
Said Defoe afterwards: "We said before the game that we needed a good start and that's what we got.
"We knew Switzerland would be a strong side and so it's pleasing to win. It was a difficult game but we came through it well."
England: Robinson, Young, Barry, Riggott, Konchesky, Pennant, Dunn, Davis (Prutton 33), Smith, Defoe (Parker 65), Crouch (Ameobi 78).