Tom Huddlestone's 13th-minute goal put Stuart Pearce's men ahead but Aaron Ramsey levelled on 24 minutes before setting up Simon Church to put Wales 2-1 aheads four minutes later.
But Wales were pegged back when Sam Vokes turned a Taylor effort past his own goalkeeper for an own goal (35 mins).
Wales took command once Huddlestone was sent off midway through the second period, and a Vokes effort bounced back off a post five minutes from time, but England's young Three Lions scrambled over the finish line to book their place in Scandinavia.
"I think we showed with the spirit and the courage the English team have got why Wales did not want to play us and why we didn't want to play Wales.
"I think it's a shame we are not both going."
Former Toon star James Milner, who was part of the side which reached the semi-finals in 2007, admits his team were given a huge wake up call.
Milner: "Wales are a quality team and I don't want to take anything away from them.
"But it was disappointing to concede so many goals in both games.
"This could be good for us and maybe this is the wake up call we needed. There's still work to do.
"We set ourselves high standards and we're disappointed. But it's a great performance to get through and we have shown we have everything needed to go on and win the tournament."