Try a 'blur' but Dingwall says England sharpening up in Six Nations
England were 14-5 down at half-time but Northampton centre Dingwall's 63rd-minute score meant they closed to within a point at 13-14.
George Ford then edged England ahead with his second penalty of the match eight minutes from time, after the fly-half's excellent 50-22 kick secured field position deep into Welsh territory.
England then defended well to complete a 16-14 success on Saturday as they made it two wins out of two following a narrow 27-24 victory over Italy in Rome, where they also overturned a half-time deficit.
"This result against Wales will give us a massive boost because it shows that if we put on to the pitch what we want, then we can beat teams," said Dingwall.
England now face arguably the three toughest games of the Championship, against Scotland, Ireland and France, starting with a trip to Edinburgh on February 24 when the tournament resumes after a rest week.
They will be encouraged in their quest to regain the Calcutta Cup from oldest rivals Scotland by their resilience in the opening two rounds, while Dingwall's fine try against Wales is a sign of England's growing ambition in attack.
'Crazy emotions'
"Essentially the forwards were battering the door down and created space, so we as backs just had to pick it off," said Dingwall. "I just managed to put myself on the edge.
"I kept (wing) Elliot Daly inside me knowing the ball would end up with me and I could hopefully get the score.
"It's all bit of a blur but the emotions that ran through me after were crazy, everything came out of me," added the 24-year-old, who was winning just his second cap.
England have undergone a rebuild under Steve Borthwick since finishing third at last year's World Cup.
That Borthwick's side are a work in progress was evident in the opening quarter against Wales, with England dominating territory and possession but failing to score any points.
To make matters worse, England were reduced to 13 men after Ollie Chessum and Ethan Roots were both sin-binned.
Instead it was Wales who led through a penalty try and an excellent score from Alex Mann.
But England stayed in touch through No 8 Ben Earl's first-half try off the back of a scrum before denying Wales any points at all after the interval.
"We actually did a lot right in the first 10 minutes and then momentum swung against us," said Dingwall, adding: "We stuck at how we wanted to play and then the rewards started to come our way and we were able to turn that into points."
Ford, a veteran of 93 England caps, played down his own role and instead lauded full-back Freddie Steward, superbly secure under all the high balls Wales kicked his way.
"Freddie was unbelievable in the air again," said Ford. "He's worth his weight in gold in a game like that."
As for his own 50-22 kick, he added: "As soon as we got back to a one-score game at 14-8, all we needed was one opportunity. Obviously a big part of that is field position."