Two goals in the last six minutes from substitutes Adam Stansfield and Jamie
Gosling gave Yeovil victory.
It looked like it would not be the Glovers' day after Lee Johnson saw an early penalty saved, and Simon Yeo fired Lincoln ahead.
But Colin Pluck equalised after half time, and Yeovil took the lead through Stansfield's close-range strike.
Gosling secured the points for Yeovil in stoppage time.
Yeovil: Weale, Lockwood, Skiverton, Rodrigues, Pluck, Williams, Johnson, Terry, Elam, Gall, Jackson. Subs: Stansfield, Crittenden, Collis, Edwards, Gosling.
Lincoln City: Marriott, Bloomer, Morgan, Weaver, Mayo, McNamara, Futcher, Butcher, Gain, Yeo, Fletcher. Subs: Sedgemore, Pearce, May, Bailey, Frecklington.
Referee: K Hill (Hertfordshire)