The Imps went into the final day knowing victory would ensure their safety, but they slipped a defeat which, coupled with Barnet's 1-0 victory, meant they fell out of the Football League.
Lincoln fell into the drop zone on 56 minutes when referee Jon Moss pointed to the spot after veteran Jamie Clapham brought down Jermaine McGlashan. Aldershot midfielder Danny Hylton sent Lincoln keeper Elliott Parish the wrong way and silenced the 7,000 home fans.
The home faithful started heading for the exit when Luke Guttridge burst through the heart of the Lincoln defence and blasted the ball past Parish on 69 minutes.
Imps manager Steve Tilson sent on former Middlesbrough striker Ben Hutchinson, but there was no way back for Lincoln.
Seventeen-goal striker Ashley Grimes blasted over during a rare Lincoln attack, but City were put out of their misery on 86 minutes when Guttridge added his second with a neat finish.