ENGLAND 2 SWITZERLAND 0
1. Joe Hart
2. Nathaniel Clyne 68'
5. Gary Cahill
6. Chris Smalling
3. Luke Shaw
7. James Milner
4. Jonjo Shelvey 57'
8. Fabian Delph 3'
11. Alex Oxlade-Chamberlain
10. Wayne Rooney
9. Raheem Sterling
Subs
16. Phil Jagielka
20. Ross Barkley 3'
15. John Stones 68'
19. Ryan Mason
17. Jamie Vardy
14. Theo Walcott
18. Harry Kane 57'
12. Kieran Gibbs
13. Jack Butland
21. Tom Heaton
Rooney had toiled throughout the Euro 2016 qualifier against the Swiss but eventually found the net from the penalty spot in the 84th minute after Raheem Sterling was fouled in the box.
The England skipper rifled a fierce shot past Yann Sommer from 12 yards to break Charlton's 45-year old record.
The match may have been a dead rubber and the goal may have come by the easiest means, but that should not detract from what is a truly remarkable achievement from Rooney.
There has been much debate in recent months about whether Rooney deserves to be classed as an England great.
But he can now look at the history books and point out to the doubters that he stands above the likes of Gary Lineker, Alan Shearer, Sir Geoff Hurst and now Charlton in the goal charts.
Given that he is 29 years old, few would bet against the captain going on to score many more.
For so long it looked as if Rooney's big night was going to end up being an anti-climax. The Manchester United forward struggled to make an impact, and England looked to be heading for a bore draw.
But Harry Kane stepped off the bench to put England ahead and Rooney blasted home a historic second to give the Three Lions the win that maintains their 100 per cent qualifying record and seals their place at the top of Group E with two matches to go.
Rooney was accompanied on to the pitch for his big night by mascot Romeo Beckham.
England could have done with a sprinkling of magic from the youngster's dad, David, in the opening stages as Wembley played host to one of the dullest halves of football in its eight-year history.
An early injury to Fabian Delph, who hobbled off with a hamstring problem, did not help.
Roy Hodgson had to re-jig his team, with substitute Ross Barkley now in the XI.
Rooney tried his best to make an impact, buzzing around up front, but Sommer remained untested.
Rooney tried - and failed - to divert Gary Cahill's header past the Swiss stopper from close range and then rolled a low shot wide.
Excitement grew temporarily when Rooney's legs started pumping on a rare charge at the Swiss defence, but he selflessly laid the ball off to James Milner and he could not beat Sommer.
The Swiss looked the more dangerous side and Joe Hart snatched the ball from Xherdan Shaqiri's feet after he had been slipped in by Granit Xhaka.
After the restart England began with more purpose. Rooney headed into Sommer's hands and Sterling used every trick in the book to try to get past his marker.
But the Swiss still had the better chances and Hart reacted quickly to deny Xhaka.
Hodgson then brought Kane on for Jonjo Shelvey. The England manager had to wait 10 minutes, rather than 79 seconds, for Kane to find the net but he did not mind - finally the drab game had a goal.
Rooney touched the ball to Luke Shaw, who picked Kane out with a precise pass to the back post and he drove low into the net.
When Sterling was brought down by Timm Klose, Rooney had the perfect opportunity to make it a fairytale and he did not waste it.