The architect of the victory was Moore’s son, Ian Thomas-Moore, who fired in a hat-trick to end his personal goal drought and hand caretaker boss Andy Liddell a dream start.
The Millers were two up in 15 minutes with poor defending allowing Thomas-Moore and Danny Harrison to score easy goals. But they really took off in the second half as a defensive error let in Thomas-Moore, who found the top corner in the 50th minute.
Three minutes later, Ryan Taylor thumped home a shot from inside the box.
The Imps’ problems worsened on the hour when centre-back Patrick Kanyuka received his second yellow card for a foul on Thomas-Moore, who sent Elliott Parish the wrong way from the resulting spot-kick.
Lincoln’s misery was not over, though, as Liddell’s men added a sixth when substitute Jason Taylor found the net from 25 yards late on.