Vadaine Oliver was the hero for the Blue Square Premier battlers, coming off the bench to score twice in extra-time and hand the Saddlers a first-round replay defeat.
The 20-year-old former Sheffield Wednesday player headed an Alan Power corner firmly into the net 12 minutes into the additional period at the Banks's Stadium and intercepted a James Chambers back pass to poke in his second and Lincoln's third two minutes from the end.
Walsall, without a win in 11 games, pulled one back through a deflected Jamie Paterson free-kick in stoppage time, but it was mere consolation.
Lincoln took the lead in the 50th minute when Power beat the offside trap to shoot past David Grof, and the Saddlers thought they had a chance of going through as Richard Taundry fired low into the net from the edge of the box to equalise nine minutes from the end of normal time.
Walsall piled on the pressure but Andrew Boyce was a tower of strength at the heart of the visitors' defence.
Lincoln now have a home tie with Mansfield in the second round.