Briscoe is Mansfield cup hero.
Louis Briscoe The Stags went in front thanks to an early own goal from luckless Imps keeper Paul Farman.
Adam Smith's lob then levelled the tie five minutes before the break.
But Anthony Howell set up Briscoe to lash home on 77 minutes to set up a lucrative home clash with the seven-times FA Cup winners on January 6. An inflatable cover, under which hot air was blown onto the playing surface, ensured that the game went ahead as scheduled at Field Mill.
If that was down to good planning, Mansfield's next slice of good news was down to good fortune when they went ahead on 14 minutes.
John Dempster's header from Chris Clements' free-kick looped over Farman before hitting the base of the post and deflecting back into the net off the Lincoln keeper's shin.
But Smith levelled five minutes before the break when, from Daniel Gray's long, hopeful hoof forward, he showed excellent poise to lob the awkwardly bouncing ball over stranded home keeper Alan Marriott, b ut then came Briscoe's winner.