The victory saw England extend their excellent recent record against Wales, having now won eight of their past 10 Six Nations meetings, and they will take on France and Ireland in their last two fixtures.
The defeat for Wales, coming after a crisis meeting with rugby bosses averted a player strike over contract issues, condemned them to a third straight opening Six Nations defeat for the first time since 2007, having already lost to Ireland and Scotland.
In a tight match that featured a lot of aimless kicking and little creativity, England had led 8-3 at the break thanks to an Owen Farrell penalty and Anthony Watson try, while Leigh Halfpenny scored a sole penalty for Wales.
A Louis Rees-Zammit intercept try, converted by Halfpenny, kickstarted the second half before England responded through a Kyle Sinckler try, converted by Farrell.
Block-busting centre Ollie Lawrence bagged England's third try four minutes from time to seal the win.
In a frenetic opening to what had been described as a pivotal game for both sides, England worked the ball through hands while Wales countered with two turnovers and clearing kicks for more defensive duties.
The deadlock was broken by a Farrell penalty from 45 metres.
The helter-skelter nature of the game continued and with Wales failing to discover any real front-foot attack or spending any time in English territory, it was the visitors who further capitalised.
The ball was moved left after a Lawrence midfield bust, Alex Dombrandt sending out a beautiful pass to Watson, who dived into the corner despite Halfpenny's attempted tackle. Farrell's conversion came back off the post.
Halfpenny pulled back a penalty for Wales, but another was spurned after Tomos Williams opted to take a quick tap that came to nothing.
Aerial dominance
An aerial contest had been expected and so it came.
However, the England back three of Steward, Max Malins and Watson were unperturbed by Wales' kicking game, proving to be totally dominant in the air.
Amid repeated refrains of "Swing Low, Sweet Chariot" from a sizeable English contingent in the 74,007 crowd in Cardiff, Wales showed little creativity and no ability to build effective pressure.
Rees-Zammit briefly threatened to turn the tide as he streaked through, only to be hauled down within reach of the line.
The ball was recycled, but Dombrandt was on hand to win a crucial penalty at the breakdown for England, Farrell clearing. Lewis Ludlam was then the key defender as Adam Beard again clung on in the ruck as Raynal blew for half-time.
The second period opened with a bang, Rees-Zammit picking off a Henry Slade pass not two minutes in for an easy run to the line. Halfpenny converted and, against all the odds, Wales were 10-8 up.
England, however, responded immediately, battling their way up to the line for Sinckler to burrow over from close range.
A raft of replacements took the sting out of the electric start to the second half.
Farrell's off day with the boot continued when he shanked a third kick at the posts that would have taken England two scores clear.
After some sustained English pressure, the Welsh defence was broken for a third time.
Replacement scrum-half Alex Mitchell worked the ball left after numerous forward drives before Steward delivered a brilliant pass to play in Lawrence, one-handed, in the corner to break Welsh hearts.
