Joseph said that England believe they have the strength and talent to take on any side in World Cup year.
"It's incredible. No greater feeling to come here to Wales and win, probably one of our greatest rivals," he told the BBC.
"But the boys dug deep and got the win we deserved. There's a lot of confidence in the side and we've got the belief we can attack and penetrate.
"The first game in this championship is massive and to get off to a winning start is huge for us."
Wales captain Sam Warburton admitted his side fell off the pace after the interval.
"We're very disappointed, it's not the start we wanted. The second half we struggled to get momentum and it seemed like England were on top for large parts," he said.
The victory, coming after the 30-3 humiliation England suffered in the corresponding fixture two years ago, sets up the World Cup it hosts nicely, with the English drawn in the same tough pool as Wales, Australia and Fiji, with only two teams qualifying for the knock-out phase.
Halfpenny opened the scoring early for Wales, booting a touchline penalty in the second minute after Jonny May infringed.
English woes were compounded after a messy first scrum, re-set by French referee Jerome Garces.
Later, Mike Brown was left with no room but dinked in a grubber behind Halfpenny to which Watson latched on to cross the whitewash for his maiden international try.
Ford's conversion came back off the posts, but Halfpenny made no mistake with his second penalty from the left touchline close to halfway.
George North went off for a concussion check after clocking a full-blooded kick to the head by English lock Dave Attwood that went unpunished by Garces, who had already awarded the visitors a penalty duly kicked by Ford.
Halfpenny missed a chance to restore Wales' lead, but Biggar fell back into the slot to nail a majestic 40-metre drop-goal on the stroke of half-time to leave Wales 16-8 up.
England started the second period just as the home side did the first and went on to score 13 unanswered points.
After going through 20 phases in the Welsh 22m area, Joseph replicated his outstanding form with Bath by jinking his way through weak tackles by Webb and Biggar for a fine try converted by Ford.
Wales winger Alex Cuthbert produced a great try-saving tackle on flanker James Haskell, but was then shown a yellow card for failing to roll away.
Ford later kicked two penalties for a deserved England win.
- AAP
