Shaw scored twice, while Jess Park and Mary Fowler also found the target in a comfortable win for Gareth Taylor's side.
Manchester City were dominant against Leicester City from the first minute and recorded a thumping win in the WSL to extend their impressive start to the season and bounce back from their damaging defeat to Chelsea.
City remain second in the WSL table but this was a morale-boosting victory that was never in doubt from the off.
City had the lead within two minutes, as Khadija Shaw headed home from within the six-yard box after a fine cross from Kerstin Casparij.
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Their second came from a similar pattern, but a different flank, as left-back Leila Ouahabi delivered another excellent ball for Shaw to finish and make it 2-0.
Jess Park scored a third early in the second half from range, and Mary Fowler added a fourth with a superb half-volley after a botched Leicester clearance.
Before full-time, Jill Roord went down and required treatment before going off. She was not replaced and City finished the game with 10 players, with her withdrawal seemingly a precaution.
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