The Silkmen levelled through ex-Iron Paul Harsley, but Lincoln held on to book their place in Saturday's play-off final at the Millennium Stadium in Cardiff.
Boss Keith Alexander said: "It was always important to get the first goal. I'm very pleased we got it, I wanted to try and take the game to them.
"Obviously, in the last 15 minutes they put us under a bit of pressure. You are always worried at 1-1."
They will meet Southend, who booked their place in the final with a 1-0 win over Northampton.
Freddy Eastwood scored the winner from the spot early in the second-half, with it being the only goal across both legs of the tie.
The former Iron target admitted: "When the ref pointed to the spot the pressure was really on me.
"I felt a little nervous but fortunately their goalkeeper moved a little early and I was able to pick my spot.
"It was a great feeling to see the ball in the back of the net and now I am hoping that we can finish our season in style at the Millennium Stadium."
Hartlepool and Sheffield Wednesday will meet on Sunday in the Leage One play-off final, with the winner going up to the Championship.