Lancaster deserved their lead, Matthew Blinkhorn heading in Ryan Winder’s cross in the twelfth minute.
Basford’s best spell during the first half came when Courey Grantham saw his 33rd minute shot deflected wide, Paul Dugdale clearing Nat Watson’s header off the line from the resulting corner.
Basford piled on the pressure at the start of the second half and Deon Miekle levelled in the 62nd minute, heading in James Reid’s free kick at the far post.
Blinkhorn almost punished defensive hesitancy with nine minutes to go, his shot coming back off the post.
Two minutes after that let-off Basford were in front, Meikle again heading in from a Reid free kick, this time from ten yards.
Basford substitute Kole Lambert made the game safe in the second minute of added time, turning a defender before despatching a low shot into the corner.