A tight game was effectively decided by Jones’s decision to trip England hooker Dylan Hartley late in the first half because while the lock was in the sin-bin England scored 17 points, with tries by James Haskell and Danny Care, to open a 20-3 lead.
Tries by Adam Jones and James Hook closed the gap to three points but a second score by Haskell, combined with the faultless goalkicking of Jonny Wilkinson (15 points), brought England home.
After their poor showing in the November internationals it was a welcome victory for England manager Martin Johnson but his side still have much to do if they are to challenge for their first Six Nations title since 2003.
“I thought we played well at times and at times we didn’t,” said Johnson. “When they came back into it we were under pressure but I was happy with the way we responded.
“Ultimately we finished it. Two years ago we were in similar circumstances and lost so to get 30 points against Wales is a goo4d start.”
Wales showed flashes of brilliance but made too many basic errors and gave themselves too much to do after Alun-Wyn’s moment of madness.
The match was preceded by various musical celebrations to mark the centenary of internationals at Twickenham, with Wales the first visitors 100 years ago.
The opening 30 minutes were something of a mess with both sides struggling to put together any cohesive movement.
Wales decided to let Hook take two penalties but he missed both, leaving England to claim a 3-0 lead with a Wilkinson penalty.
Wales, seeking their fourth successive championship victory over England, levelled when Stephen Jones took over the kicking duties before Alun-Wyn was sinbinned.
England immediately piled on the pressure and made it pay when flanker Haskell barrelled over for the first try.
Wilkinson converted to give England a 13-3 halftime lead.
The hosts wasted little time in extending that lead as captain Steve Borthwick stripped the ball away in the tackle to set up a move that ended with scrumhalf Care scampering over for a try.
Wilkinson converted for a lead of 20-3.
Buoyed by Alun-Wyn’s return Wales hit back as prop Adam Jones found himself as the last man on a left wing overlap and flopped over the line for a converted try after 49 minutes.
Twenty minutes of chaotic rugby followed with neither side able to take a grip and Wales, in particular, guilty of too many basic errors.
From nothing, however, Wales hit back as Hook, in his first start at outside centre in his 38th appearance, ripped through the English midfield to score a superb try.
Stephen Jones’s conversion closed the gap to three points but just as the Welsh fans were sniffing a famous comeback, Delon Armitage intercepted a Welsh pass and sent Mathew Tait clear.
Tait, at fault for Hook’s try, kept his head to flip an inside pass to Haskell to score his second try.
England next travel to Italy on Feb. 14 while Wales host Scotland on Feb. 13.
“The most disappointing point was conceding 17 points when down to 14 men. We’d talked all week about discipline but that was game over,” Wales coach Warren Gatland told the BBC.
“It was absolutely stupid what he has done and it’s probably cost Wales the game today.”