England pounced on a number of defensive mistakes made by the Danes, who failed to punish a string of England errors, although Nicolai Jorgensen had a goal wrongly ruled out for offside.
Injury-plagued captain Richards, a regular with FA Cup and Champions League-qualification chasing City this season, was replaced by West Ham's James Tomkins.
The visitors took the lead in the 23rd minute when Michael Lumb, under no pressure, managed to head the ball straight to Welbeck.
Sunderland's on-loan Manchester United striker took a touch 25 yards out before hitting a looping left-footer into the roof of the net.
England were clinging on before half-time, but Denmark shot themselves in the foot again in the 58th minute when Sturridge's 30-yard curler was parried by Jonas Lossl straight to in-form Swansea striker Sinclair who prodded home without fuss.
Bolton's on-loan Chelsea forward Sturridge soon got the goal his performance deserved four minutes later when he bamboozled Erik Sviatchenko before sliding the ball home from 10 yards.
Pearce made a host of changes with Monday 's friendly against Iceland in mind before Henderson turned well to fire in a close-range fourth to add a late gloss.
"I was disappointed with the performance in the first half to be honest," said Pearce.
"In the second half I thought it improved greatly. The main thing for me tonight was to learn something about the players.
"I thought Sturridge was outstanding this evening and the goalkeeper [Alex McCarthy] has come in for his first full start and done extremely well."
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