Argyle created chances early on, as Reuben Reid had a headed effort from within the six-yard box well saved.
The hosts grew into the tie and went close when Nick Wright saw his effort parried away by Jake Cole.
Luke Young had the best opportunity late on when his dinked ball over the Imps keeper was inches off target.
The replay will take place at Home Park on Wednesday, 20 November.
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Lincoln City manager Gary Simpson told BBC Radio Lincolnshire:
"I think we played okay again. The opportunities that we've had, we just couldn't put away. It was tight and they came into the game late on as we tired a bit in midfield but I think a draw was a fair result.
"Sometimes we fell asleep and didn't pick the runners up but overall we acquitted ourselves quite well. A better ball into the box might have given us some reward but it's another tie and more money in the coffers but we're doing it the hard way."
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Plymouth Argyle manager John Sheridan told BBC Radio Devon:
"We had good possession of the ball, especially in the second half, and I think if we'd used it a lot better, we could possibly have got one or two goals - but I was pleased with the way we played.
"I thought he [on-loan striker Tope Obadeyi] came on and looked sharp and bright. He's very quick and he'll give us that threat in behind, and I thought he did well. He only met up with us last night so full credit to him.
"Our form's not too bad at the moment - we've got to make sure we get through and I'll expect another tough game, but we're at home and I expect us to win."
Conference Premier side Lincoln City battled to a goalless draw against League Two Plymouth Argyle in the first round of the FA Cup.