Nigel Starkey's side were ahead in the 14th minute when good work from Tom Rawlings on the left saw him drag the ball across the goal to give Bradley Taylor a simply tap-in.
Sphinx had the better of the chances but it was not until the fifth minute of the second half that they doubled their tally thanks to another cross from Rawlings again being slotted home from close range by Bradley Taylor.
Playing some good football ahead of their FA Youth Cup tie at Kidderminster Harriers next Thursday, Coventry Sphinx added a third on the hour mark thanks to a looping header from Chris O'Shea.
With Alvechurch were down to ten men following a reckless challenge, Sphinx went to town.
The visiting keeper looked to have caught the ball in the 74th minute but allowed it to spill out of his grasp and the ball fell for substitute Joe Cadden to tap home for the fourth.
Cadden was presented with another tap in four minutes from time and made no mistake from close range.
In the last minute, a drive by Tom Rawlings gave Sphinx a sixth goal and wrapped up a good night's work.