Rooney overshadows Owen
England looked nervous in the opening exchanges of the match in Coimbra, and struggled to maintain possession in the late afternoon heat.
A disjointed England side finally got their act together on 23 minutes when Steven Gerrard piled forward before laying the ball off to David Beckham.
The England skipper's floated cross found Owen at the far post and he crossed for Rooney to make history and settle the nerves of Sven Goran Eriksson's side.
England defended well throughout the match but seemed to lack imagination at times, and the nerves were always just underneath the surface as the game wore on.
The game swung in their favour on the hour mark when Russian referee Valentin Ivanov sent off West Brom right back Bernt Haas.
Haas had fully deserved his first yellow card for a nasty tackle on Steven Gerrard, but his second challenge on Ashley Cole seemed less worthy of a booking.
The official had no such doubts, however, and quickly sent Haas for an early bath, leaving England in control.
They still failed to dominate the ten men of Switzerland, but Wayne Rooney's second strike, which came off the post and the keeper's head, sealed the game.
Gerrard capped a good day's work for Eriksson's men by slotting in a third after a good move down the right by Beckham and Gary Neville.
Although England are now back on track there will still be some worries for Eriksson, firstly their failure to control possession of the ball, even against ten men - and the form of Owen.
Owen chipped in the cross for Rooney to become the tournament's youngest ever goalscorer, but the form of the Liverpool man must be a worry to England fans.
It is not Owen's lack of goals in the opening two games that is a worry for Sven Goran Eriksson, but his anonymous displays in both games.
He has been replaced twice by Darius Vassell who has looked a bundle of energy and has troubled both France and Switzerland's rear guards.
Owen has hardly had a sniff at goal and while the whole country will be rejoicing in Rooney's exploits, they will be also be hoping to see more of Owen as the tournament progresses.
England take on Croatia in their final Group B match and will be desperate for Owen to get on the scoresheet, or at least be more involved.
Like any other striker Owen thrives on confidence, but he seems to be lacking just that at present. His first touch as not as good as it could be and he lacks the drive to go past players and get shots in on target.
All of England will be hoping it is just a slow start, and a scrambled effort that bounces off him may just spark him into life.
Owen has been England's man for the big occasion for the past few years, but his place in the limelight is now being taken over by Rooney.
Maybe opposition defences will pay more attention to Rooney and afford Owen more space, but whatever it takes England will need Owen at some point during this tournament if they are to go all the way.