Lincoln City 1-0 Southport
Tom Miller's first-half header for Lincoln was enough to seal victory against Southport.
The midfielder nodded home from close range, latching onto Sean Newton's cross from the left wing.
Southport goalkeeper Danny Hurst denied the hosts a late second, frustrating Nick Wright from the penalty spot after James Smith was fouled.
Earlier, Lincoln keeper Paul Farman protected the hosts' lead, tipping Scott Brown's effort around the post.