Battling City suffered a late defeat at Portsmouth despite a strong performance at Fratton Park.
City edged the first half, but trailed thanks to a converted penalty from George Hirst and a stunning free-kick from Michael Jacobs.
A sublime move finished by Ted Bishop gave the Imps hope, with Ben House's first strike for the club - just 30 seconds after coming off the bench - drew the visitors level.
But Lincolnshire hearts were broken in the closing stages as Ronan Curtis struck a late winner.
Attendance: 15,175 (811 away)