The game got off to a good start for the visitors with the Avon Keeper saving well from Jimmy Howard in the second minute of the game.
In the fifth minute Warren Gerrard linked up well with Jamie Cardwell in midfield and his pass found Martin Dearden in space on the left; Dearden cut inside beating two defenders before rounding the Avon, keeper and slotting the ball home.
Seven minutes later Jordan Hallwood put in a great cross from the left that was met by a Howard volley which somehow was cleared off the Villa line.
Avon pressed but their best efforts were easily dealt with by Danny Still in the Billinge goal.
The Storks were dealt a blow in the 35min when Gerrard had to be replaced after picking up a back injury.
Two minutes before half-time the home side broke through the New St defence but the quick reactions from Still forced the Avon striker to fire his shot over the ball.
In the second-half both Dearden and Howard kept the pressure on the home defence, and in the 65th minute Connor Simpson's through ball found Howard who raced through on goal only to be taken out by a desperate late challenge on the edge of the box.
The resulting free kick saw the Avon keeper save well.
In the last 20 minutes Avon mounted the pressure on the Billinge defence but the well organised red wall led by Scott Maher kept Avon out and gave the well-earned three points to the visitors.
After the game manager Steve Hallwood said: "I thought it was a good match to be fair.
"I felt it should have been more comfortable, but a win is a win and I'm particularly happy with our third clean sheet in five games."
Billinge New Street are next in Cheshire League action when they play Wythenshawe Reserves in a 2.30pm kick-off at Sutton Leisure.