Ramsey was really into full flow and after 32 minutes his cross-field ball found Joe Ledley, with the Cardiff man striking his cross to the near post for Church to turn past David Marshall.
Three minutes later Wales had their third - a stunning solo goal from Ramsey.
He went past Stephen McManus and Darren Fletcher in a superb run from midfield before driving a low effort beyond Marshall.
The Cardiff goalkeeper then kept out a close-range drive from Ledley as Wales continued to press forward.
By the interval, the Scots were in shock. Their fans booed when Burley's picture appeared on the giant television screens and the team were jeered off.
Wales brought on Sam Vokes and Robert Earnshaw for Church and Ched Evans, and within a minute Marshall was lucky not to be dismissed when he rushed out of his box and handled a Vokes chip.
Swiss referee Cyril Zimmermann decided the challenge was only worthy of a yellow card.
Scotland sent on Steven Fletcher for Miller and Lee Wallace for Fox, while Wales took off Ramsey to give Joe Allen a run in midfield.
Scotland must have been pleased to see the back of Ramsey, who was clearly being rested with a vital midweek under-21 game in Bosnia in mind.
Wales then felt able to give Danny Gabbidon a run-out in defence in place of Lewin Nyatanga, as the West Ham defender returned from two months out with a calf injury.
The rotation of substitutes continued with the Scots replacing Steven Naismith, McFadden, Graham Dorrans and Don Cowie with Ross McCormack, Kevin Kyle, Barry Robson and Derek Riordan but Burley's side only marginally improved.
Hennessey had not been really tested, although he did have to turn over a McCormack chip and block a Riordan drive in the closing 10 minutes.
Wales also rang the changes but did not relinquish control of the contest as Scotland were left to contemplate an embarrassing loss.
Wales: Hennessey, Ricketts, Nyatanga (Gabbidon 60), Williams, Morgan, Bale, Ledley (King 80), Ramsey (Allen 56), Edwards (Cotterill 88), Evans (Vokes 46), Church (Earnshaw 46).
Subs Not Used: Brown, Easter, Dorman, Matthews, Blake.
Goals: Edwards 17, Church 32, Ramsey 35.
Scotland: Marshall, Hutton, McManus, Gary Caldwell, Fox (Wallace 54), Dorrans (Robson 71), Darren Fletcher, Cowie (Riordan 78), Miller (Steven Fletcher 55), Naismith (McCormack 62), McFadden (Kyle 62).
Subs Not Used: Langfield, Gallacher, Berra, Steven Caldwell, Adam.
Ref: Cyrill Zimmermann (Switzerland).