Two goals in three first-half minutes swung the game in the table-topping Millers’ favour as they secured a seven-point cushion over third-placed MK Dons.
Rotherham ended a rare three-game run without victory but were made to hang on at the death by the Imps.
Ben Wiles should have put the home side in front early on. The midfielder was all alone at the back post from Mickel Miller’s cross but fired straight at Lincoln goalkeeper Jordan Wright.
But he made no mistake in the 11th minute after being picked out by Ollie Rathbone, sliding his effort in off the post.
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Wiles led another Millers attack in the 13th minute, with Chiedozie Ogbene finishing it off superbly into the same bottom corner to double the lead.
Lincoln improved in the second period and Tom Hopper should have halved the deficit but he blazed over from close range.
Hopper did take the next chance that came his way, sweeping home from Cohen Bramall’s cross in the 81st minute to set up a nervy end for the home side.