Martin Johnson's men raced into a 13-7 lead at the interval and survived a second-half Welsh fight back.
George North struck early for the visitors but England hit back with tries from James Haskell and debutant Manu Tuilagi.
Shane Williams and North struck with second-half tries for Wales but it was not enough with the boot of Jonny Wilkinson guiding England to victory.
But the game could come at a heavy cost for both sides. Morgan Stoddart, a late replacement for Stephen Jones, was carried off with a broken leg while England captain Lewis Moody had to be helped off with what looked like a reoccurrence of his troublesome knee injury.
Wilkinson opened the scoring with a well-struck penalty on five minutes but Wales took the lead thanks to North after going through 17 phases on 17 minutes.
Priestland added the extras but an dominant England scrum saw Haskell crash over on 25 minutes.
Wilkinson added made no mistake with the conversion and added a drop-goal to hand the hosts a 13-7 half-time lead.
It took just three minutes of the restart for Tuilagi to power over, cutting a brilliant angle off Jonny Wilkinson to score despite the last-ditch efforts of Stoddart.
Moments later the Scarlets wing was stretchered off in a leg brace and on oxygen after falling awkwardly in the tackle.
But dragged themselves into the game on the 56th minute when Williams raced into the corner for his first ever try at Twickenham.
Wilkinson added a second drop-goal before North grabbed his second, following a fine Sam Warburton break. Priestland converted to set-up a tense finale but England held on for a hard-fought victory.