England 30 Wales 17
But there were many uneasy moments for Johnson to endure as Wales threatened a stirring revival from 20-3 adrift.
They got to within three points before England flanker James Haskell's second try — sparked by a Delon Armitage interception — meant Johnson could finally breathe easily.
Tries either side of half-time from Haskell and scrum-half Danny Care put England in charge, and Jonny Wilkinson completed the job with 15 points from his left boot.
It meant England staved off a fourth successive Six Nations defeat against Wales.
Wales, whose last Twickenham visit in 2008 kick-started a Grand Slam campaign, fell short of the standards demanded by head coach Warren Gatland, despite tries for prop Adam Jones and centre James Hook.
Their line-out was a shambles, and lock Alun Wyn Jones's first-half yellow card for foul play saw England critically score 17 points in his absence.
Stephen Jones kicked a penalty and two conversions, yet an often inaccurate Wales were ultimately punished.
England, for all the bold suggestions of a sharper attacking edge through Care, Armitage and centre Mathew Tait, never threatened to hit top gear.
But in truth, they did not have to, as Wales made far too many mistakes to be competitive at the business end of a frustratingly error-strewn encounter.
Wilkinson booted England into an 11th-minute lead after Wales forward Andy Powell was punished for being off his feet in a ruck, yet there remained little to choose between the sides.
England had started to exert some dominance at the line-out, taking three of Wales's first five throws, but their indiscipline at an attacking scrum — prop David Wilson was punished — blew a promising position.
Wales had two long-range penalty chances during the opening 22 minutes, yet both were sent wide by Hook as neither team settled.
Jones replaced Hook when Wales gained another long-range chance 13 minutes before the break, and he found the target with an equalising strike.
But England finished the half totally in charge, helped by reckless foul play from Wales lock Jones.
His trip on England hooker Dylan Hartley had a deflating effect on his team, who conceded 10 points in his absence.
Wilkinson applied an immediate punishment, kicking the resulting penalty, but worse was to come for Wales as Jones pondered his woeful indiscipline from his seat in the stand.
Despite some heroic defensive work, especially from Wales prop Adam Jones, Wales could not hold England out and Haskell stretched over for a close-range try.
Wales initially did well to thwart England's efforts, before Haskell squeezed through the combined challenge of scrum-half Gareth Cooper and Wales captain Ryan Jones.
Wilkinson added the conversion, lifting England into a 13-3 lead and underlining Jones's crass indiscretion.
But worse was to come for the Ospreys lock as England scored again before he could return to the field.
England skipper Steve Borthwick stole possession superbly for his side, creating an attacking platform that Care prospered from by racing through an absent defence.
Wilkinson's conversion put England 20-3 ahead, and Wales knew they had to score next or face oblivion.
But the visitors delivered, Jones going a small way to atoning for his sin-binning by delivering the scoring pass to prop Jones that gave Wales a glimmer of hope.
Hook then increased Welsh optimism with a darting score, but England finished them off when a Stephen Jones pass was intercepted and the home side broke 60 metres upfield to score.
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