Aaron Ramsey's through pass was intercepted by Chelsea youngster Mancienne but his hacked clearance ricocheted off Newcastle's Taylor.
Both left it for each other and Reading striker Church made the most of their indecision with a composed finish to score Wales' first ever goal against England at this level.
A defensive howler from Wales gifted England their leveller just six minutes later.
Middlesbrough defender Wheater rose unchallenged to head Jamie O'Hara's deep right-wing corner past Wales defenders Rhoys Wiggins and Andy King into the net.
Aston Villa star Agbonlahor hit the bar and James Milner and Johnson tested Welsh keeper Owain fon Williams before the visitors took a deserved lead.
Mark Noble's defence-splitting pass set Johnson free and the Middlesbrough winger skipped around Wales captain Neal Eardley before firing past fon Williams.
The Premier League stars of England seemed comfortable against a Wales team made up of mostly lower league unknowns, with the exception of Arsenal midfielder Ramsey.
Wales' teenage star showed why Gunners boss Arsene Wenger paid £5m for him in the summer when his cute pass set up Church for his second.
The 19-year-old, on loan at Wycombe Wanderers, cut inside Taylor before unleashing a left-foot drive past helpless Manchester City keeper Joe Hart.
Simon Church has scored six goals in nine Wales Under-21 games
Church's double strike, his fifth and sixth goal in nine under-21 games, was particularly special bearing in mind England had conceded just once in their eight qualifying games.
England's top-flight experience showed after the restart as Stuart Pearce's team began to dominate and striker Agbonlahor made their possession count just after an hour.
Noble's run and cut-back from thy byline was cheekily back-heeled into Wales' net as the Villa goal-scorer converted his sixth already this season.
Shaun MacDonald and Ramsey went closest for Wales in the second-half from long range, the Swansea winger stinging the hands of stopper Hart.
Wales - minus nine senior team call-ups including Gareth Bale, Ched Evans and Chris Gunter - continued to probe but Noble's 25-yard shot ensured Pearce's England remained on top.
However, in the battle of the West Ham United midfielders, Jack Collison had Hart worried late on as his shot flew narrowly over.
Wales were beaten but not embarrassed by their illustrious opponents and showcased the strides they have made under boss Flynn.
Wales U21: fon Williams, Eardley, Blake, Nyatanga, Wiggins, Adams (Allen 59), Collison, King (James 84), MacDonald (Brown 76), Ramsey, Church. Subs Not Used: Taylor, Jacobson, Mike Williams, Marc Williams.
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