The Pirates as a strikeforce were simply too powerful for the Red Imps who failed in the League Two play-offs for a fifth consecutive season.
A pulsating game went Rovers' way right from the start with skipper Stuart Campbell blasting in from 30 yards to punish the home team for giving the ball away in the third minute.
Rovers then tore Lincoln apart over the next ten minutes. Rickie Lambert should have scored when he beat Lincoln's Lee Beevers inside the box, but his shot was too close to keeper Alan Marriott.
Rovers, who were already 2-1 ahead from the first leg, went even further in front in the 11th minute. Richard Walker was left with too much space on the left and crossed for Lambert to score from close range.
Ryan Green then set up Lambert for another easy chance but, although the striker's header beat Marriott, Lincoln were saved by the post.
The disastrous early spell meant Lincoln could only dream of what might have been for the remainder of the game.
They got on the scoresheet witn their first meaningful attack when Jeff Hughes fired in from six yards in the 25th minute.
But Rovers powered back in response and were quick to restore their three-goal aggregate lead. Lincoln's defence made a mess of clearing a 36th-minute cross and Walker made them pay when he shot home.
Lincoln were not finished and Mark Stallard found the net from inside the box two minutes before the break.
Rovers were content to soak up the pressure in the second half and hit Lincoln on the break. The tactic worked perfectly and they caught Lincoln out in the 82nd minute when Sammy Igoe was left unmarked and sidefooted home.
Ex-Pirate Jamie Forrester was unlucky four minutes later when his shot came back off the bar, but Lincoln were well and truly sunk in the 90th minute.
Rovers sub Sean Rigg was allowed to continue despite looking yards offside and slipped his shot past Marriott.
But even then the scoring was not finished and, in the second minute of stoppage time, Hughes smashed in his second of the night for Lincoln from outside the box.