A goal in the 65th minute from substitute Abbid Uddin secured the three points for the visitors, and with Irlam MS dropping two at home to Monton, it proved to be a welcome weekend for Heys.
The result keeps alive their outside chances of winning the championship, but they did not have it all their own way as Avro were out to revenge a defeat at Sandgate a couple of weeks ago.
Danny Roberts in for the suspended Tommy Allen was forced to clear his lines as early as the sixth minute, as Avro centre forward Gavin chased a superb flick-on from Harris.
Ian Hutchinson, who has been excellent since coming back into the side three weeks ago, marshalled his back four superbly and was also instrumental in putting Lomax in the clear with an excellent through-ball, only for Avro goalkeeper Thomas to deny him with a fine save.
Andy Sensale, in for the out-of-favour John Garrick, benefited from the outstanding Jason Dormer in the middle, pulling all the strings and creating good chances for Howson and Colderidge.
The half ended with Avros Griffin seeing his dipping volley go past Roberts post.
Heys emerged for the second half determined to grab the win, and within minutes of the restart a well worked move involving Slater, Dormer and Lomax ended with Colderidge hitting the inside of the post, the ball bobbling along the goaline before being cleared away,
Abbid Uddin then entered the fray for the unlucky Howson, and seven minutes later he was on hand to head the ball into a empty net, after the Hutchinson had closed the Avro keeper down and created the opportunity.
Uddin had another chance to increase his sides lead when a mesmerising piece of skill left the Avro full-back for dead and produced a wonderful save from Thomas.
Heys kept pressing for the second goal, and but for some poor finishing from Kavanagh, Sensale and Lomax they would have got their just desserts
But with Doran and Walters at the heart of the defence giving nothing away, Uddins solitary goal was enough.
HEYS: Roberts, Hutchinson, Slater, Walters, Doran, Coldridge, Kavanagh, Howson, Dormer, Sensale, Lomax. Subs: Roberts, Garrick, Uddin, Price.
l The reserves drew 2-2 draw at home with Springhead. Sixteen-year-old goalkeeper Mark Lewis, signed recently from Salford City had an outstanding debut and Mark O'Brien Jnr and Mark Denham ensured a point.
l The U15s game on Sunday at home to Woodbank was called off five minutes before kick off.
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