Alex Wills, Archie McParland, and Ioan Jones all crossed the whitewash inside the opening half hour to put the hosts in control in Bath.
But Wales fought back, responding immediately through Huw Anderson and reducing England to few chances after the break.
However it was not enough to prevent a home victory as Scott Kirk sealed a bonus point with a fourth try for the hosts just over five minutes from time.
It was a fast start at The Rec, with the English pack asserting some early dominance at the scrum.
The breakthrough came after 11 minutes, as a maul one corner opened up the space for the hosts, who exploited it with precision through the hands from Ollie Spencer and Ioan Jones before Alex Wills dived over in the corner.
Wales were immediately under pressure after the restart after Ben Redshaw charged down a kick to send the visitors back to their own 22.
It proved the the platform for England’s second try, five minutes from their first as Archie McParland found the gap after a superb offload from Craig Wright before the scrum-half rode two tackles to dot down.
Wright was involved again as England looked to press home their first-half dominance, as the hooker made a powerful break for the line after more smooth hands in the backs but he was just held up on the line.
The home side had their third try just a minute later, Wills the architect this time with a clever kick and chase out wide and Jones was close behind him with impressive footwork to pick up the loose ball and crash over in the corner on the hour mark.
Yet Wales remained a threat and got themselves on the scoreboard a minute later.
Some strong pressure from the restart sent the England defence into their own 22 and some quick ball allowed Huw Anderson to run through and score, with Harri Wilde adding the extras to close the deficit to 15-7.
That try appeared to spark greater confidence from the visitors, and they were given a further boost when Olamide Sodeke saw yellow.
They almost took advantage straight away as Walker Price and Louie Hennessy combined dangerously on the left wing but a big tackle from McParland put a halt to the attack five metres from the try line.
Much like the first half, England started the second brightly and extended their advantage after five minutes as Rory Taylor slotted home a penalty.
An attritional second half yielded few scoring opportunities for either side and it was not until after the hour that Josh Bellamy extended England’s lead to two converted tries with another penalty.
England continued to push forward in search of a fourth try but were met with resolute Welsh defence.
The best chance fell to Wills on the wing after a sublime cross-field kick from Bellamy found him in space but he was unable to finish in the corner.
The win was then sealed with six minutes left on the clock, as Kirk eventually found a gap after relentless pressure on the Welsh try line.