It is a pretty ineffective opening half from both sides, with the game failing to explode into action before the break.
The opening quarter hour has been scruffy, but the visitors, unperturbed by their long trip west, are starting to shade the possession. They briefly threaten the Church goal, with a headed goalline clearance required, and an 18th minute corner is deflected just wide of the back post - a half chance.
First sighter for Church is on 25 minutes when Ammar Dyer shoots on target from distance. But the Sudbury goal is not really under threat.
But the next chance falls again to the visitors when the ball is bouncing across the Church box; a couple of shots are blocked; the ball is finally screwed just wide.
Four minutes before the break the lead should have been Sudbury's after Archie Crowther was caught in possession on the touchline, allowing the visitors to break two on one. The ball is squared across the Church box, but the ultimate shot is screwed wide of an effectively open goal from eight yards.
Half Time : Alvechurch 0 AFC Sudbury 0
The second half begins with a good spell of pressure from the home side.
A series of corners promise to bring an opening, but shots are blocked in a crowded box, and the Sudbury goal survives.
And the visitors show that they are here to more than survive when they take the lead on 58 minutes.
Church fail to clear their lines on the edge of the box, and after what seems like an age, almost in slow motion, Joe Neal flashes a low shot unerringly into the corner of Cisse's goal.
It is a blow, and it could have been worse on 73 minutes when Cisse was forced to save bravely at the feet of a Sudbury forward after quick feet from Lewis had created an opening.
Church's second half substitutions proved to be watershed moments, with Onabirekhanlen, Ngandu and Sullivan all injecting new impetus into Church's quest for an equaliser.
Ngandu finds himself behind the Sudbury beck line on 75 minutes, bearing down on the advancing keeper Bradbrook, and it is the Sudbury man who comes out on top this time in making a good blocking save.
But three minutes later he is not to be denied. His initial shot is blocked, Sullivan tries to make something of the loose ball, but is grounded, and then Ngandu steps in to steer a second effort deftly into the top right hand corner of Bradbrook's goal.
It's a deserved equaliser, and the points are anybody's now.
And Church seem to be wanting them more , with Dyer bringing a good save from Bradbrook on 84 minutes after unleashing a 25 yard shot, and Sullivan curls the re-cycled ball just over.
Church finish the game the stronger, but run out of time to make their increasing dominance count, and the relegation haunted Suffolk side escape back down the A14 with, for them, a precious point