Brackley made it back to back wins after coming from behind to beat Boston 2-1 away from home.
Oisin Gallagher gave the hosts the lead in the 44th minute.
But Brackley, who had ended a six-match losing run in the National League by beating Forest Green on Boxing Day, responded strongly after the break.
Zac Brown levelled in the 51st minute and the visitors got their winner with 16 minutes left when Ben Wodskou scored to move his side three points clear of the relegation zone.
