Boss Darren Kelly named an unchanged squad from the side who lost 2-0 on the road at Ashton United last weekend.
Boro enjoyed the first attempt on goal, top-scorer James Walshaw firing wide of the target when well-placed after eight minutes.
Walshaw wasn’t to be denied on 24 minutes, the striker was in the right place at the right time to tap in after Kieran Glynn’s initial effort was parried by United custodian Kieran Preston.
Boro’s Tom Allan and Wayne Brooksby then went into referee Daniel Pattison’s book, Brooksby also seeing a curling effort smartly saved by Preston.
The visitors almost doubled their advantage just before the interval, Allan guiding his header just wide of the target.
Basford has efforts on goal blocked on 51 and 56 minutes, James Reid and Zak Goodson the men denied by some stout defending from the visitors.
Boro ought to have made it 2-0 on the hour-mark, but skipper Michael Coulson’s header drifted wide.
The Boro skipper then saw a 35-yard strike sail the wrong side of the post as the visitors went in search of a second to kill the game off.
Shortly after being booked for kicking the ball away, on-loan midfielder Glynn saw a good effort beaten away by the gloves of the home keeper Preston.
Coulson went close yet again on 81 minutes, but he was yet again denied by Preston, who tipped the ball over his bar.
Athletic were almost made to pay for their missed opportunities in front of goal when, in the final minute of four added on by the referee, Tommy Taylor was forced into a stunning save to cling onto the three points.