The home side took the lead in the 10th minute when Ian Williams tapped in at the far post after a mix-up between Justin Whittle and Mark Greaves.
However City were back on level terms just seconds later when Nicky Mohan headed home from a free kick.
Lee Philpott had a 20-yard shot saved soon later, and then Mohan hit the bar with another thundering header from a corner in the 20th minute, but there was to be no breakthrough and the two sides went in at half time with the score at 1-1.
City re-emerged for the second half with a totally different team. Elliott, Strong, Anderson, Smith and Ashbee were all out making their debuts.
Stuart Elliott made a very impressive start, and came close to putting City ahead just 5 mintues in. He went on a long run from the half way line beating numerous Lincoln players before being stopped just as he was bearing down on goal.
Gary Alexander then shot just wide while Lawrie Dudfield looped a header over.
City finally got the goal they'd be pressing for in the 70th minute. Ryan Williams played the ball centrally to Ian Ashbee who dribbled through before threading it in for Lawrie Dudfield, who slid the ball underneath the Lincoln keeper to make it 2-1, and that's how it stayed.
First half line-up (4-3-3): Musselwhite; Whittle, Mohan, Wicks, Peat; Petty, Greaves, Philpott; Heard, Bloomer, Holt.
Second half line-up (4-3-3): Glennon; Edwards, Anderson, Strong, Smith; Price, Ashbee, Williams; Dudfield, Alexander, Elliott.