Cole was in outstanding form for the Pilgrims at Sincil Bank, with two excellent saves to deny Nick Wright in particular, as they held on for another shot against Skrill Premier Lincoln.
Wright was initially stopped by a full-stretch Cole midway through the first half while the Plymouth 'keeper bettered that after the break from a header at the near post.
Plymouth had chances of their own, with Conor Hourihane firing a free-kick straight at Lincoln 'keeper Paul Farman before Lewis Alessandra blasted at him from just inside the penalty area.
The visitors' best chance of the game fell to Luke Young with eight minutes remaining when he skipped clean through but dragged his shot wide.
Both sides tried desperately to find a winner in a bid to avoid a midweek replay but they struggled in front of goal, with Alessandra blazing well over the crossbar at the close, and must now do it all over again.