They trailed 2-0 at the break, with the Imps clinical with their finishing as United enjoyed the better build-up play but wasted chances in the final third.
On-loan midfielder Richie Ryan impressed, seeing an early free-kick come crashing off the crossbar and a header well saved.
Andy Brown also went close with an headed effort, he was replaced at the break after taking a knock on the ankle.
United were stronger in the second-half, but quickly found themselves hit on the counter attack to fall 3-0 down.
Sharp and Ryan were key in the fightback. Ryan was key in the first Iron goal, as the ball found its way back to him from a corner.
His ball in found Rob Smith, unmarked in the area as the visitors' offside trap floundered, and he poked the ball home from close range.
And Rankine added a second shortly afterwards, with a well-worked counter attack move.
But although United looked creative in midfield, they could not find a killer finish to beat the in-form Imps keeper.
In contrast, Lincoln beat Adam Capp with their only three clear chances.