A goal in each half ensured Kevin Horlock's side moved into 5th place after their third consecutive victory from their first five league matches.
The Marketmen named an unchanged side once again following Saturday's 6-1 win at Coalville Town, with Luke Ingram returning to the bench.
The opening stages of the game, in which the home side were arguably the better side throughout the first half, saw the Marketmen start brightly, Tevan Allen tried his luck at goal from 35-yards out but his strike was blocked after 4 minutes. Needham then created a great chance a minute later, Reece Harris' right wing corner was headed back into the danger area by Callum Page, at the far post, finding Dan Morphew whose close range volley was deflected crucially just over for a corner.
At the other end, Alvechurch broke forward after some neat link-up play which saw Jaanai Gordon fed through onto the right-hand side of the box whose tight angled low volley was beaten behind well by a smart near post save from Marcus Garnham on 14 minutes.
Just prior to the downpour of torrential rain, Needham broke the deadlock five minutes later. Jake Dye exploited space out on the right wing to whip a good cross into the box which took a deflection before flying into the top far corner, 1-0 Needham.
The Church meanwhile saw a good crossfield ball out to the left-hand side of the box headed into the six yard box by Yaw Namtwi-Ofosu well read by Garnham, to claim possession on 25 minutes.
Jack Hallahan then shot narrowly wide of the bottom right-hand corner on 35 minutes, while Needham saw Kyle Hammond thread Tev Allen through onto the right-hand side of the box, the midfielder's blocked shot however fell to the latter who in turn teed up Jacob Lay, but his shot was off target on 41 minutes.
As the torrential rain briefly stopped, Jacob Lay's ferocious strike forced a good save out of the visiting goalkeeper a minute later, as the first half drew to a close following 3 added minutes.
The second half saw both teams start well, as good play from Jamie McGrath saw the Needham striker hold up possession well before winning a corner five minutes after the restart.
Alvechurch meanwhile broke up the other end on 53 minutes, but the shot in space on the left-hand edge of the box was curled over the top far corner.
Reece Harris then arrived to latch onto the loose ball, following a good break from the home side on 61 minutes, but the midfielder's 30-yard strike curled narrowly wide of the bottom left-hand corner.
Chong meanwhile shot wide for the visitors two minutes later, while a superb instinctive reaction save from Marcus Garnham swatted over Kai George's close range strike after Kobe Chong's headed flick on from a left wing cross on 78 minutes.
Jack Concannon then found space inside the box from the resulting corner, a minute later, whose low shot went narrowly wide of the bottom near corner.
Needham substitute Seth Chambers meanwhile broke into space well down the right wing, but the forward's low ball squared across the face of goal, on a plate for fellow substitute Ollie Fraser was crucislly deflected behind for a corner, denying an almost certain goal on 87 minutes.
The Marketmen though wrapped up all three points in the fourth minute of seven added minutes, Ollie Fraser surged through down the left wing before breaking past the defender onto the left-hand byline to square a brilliant ball on a plate into the six yard box for Tev Allen to slide in and tap home his maiden Needham goal, 2-0 Needham.
Allen nearly made it 3-0 two minutes later, the midfielder looked to curl a good strike from inside the box into the roof of the net, but his shot was beaten over by the keeper.
Needham travel to fellow Suffolk side Leiston on Monday (28th August, 3pm).