Port Vale fans shouted for manager Dean Glover to be sacked after League Two form side Lincoln extended their unbeaten run to seven games.
The visitors were always in charge and could have scored more than the Dany N'Guessan goal that decided the game.
Scott Kerr's left-wing corner came back off the post and N'Guessan fired in the loose ball from five yards.
Lincoln had a second goal ruled out on the hour when a header by Lenell John-Lewis was disallowed for a push.
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Port Vale: Anyon, Griffith, Collins, Owen, Edwards, Lawrie, Ahmed, Brown, Dodds (Richman 85), Glover (Thompson 85), Perry (McCombe 66)
Subs Not Used: Martin, Howland.
Booked: Ahmed.
Lincoln City: Burch, Green, Beevers, Kovacs, Brown, 'Guessan, Kerr, Oakes, John-Lewis (Patulea 82), Elding (Clarke 88), Wright (Mullarkey 83)
Subs Not Used: Duffy, Sinclair
Booked: Kovacs, Oakes, Mullarkey
Goals: N'Guessan 12
Att: 5,097
Ref: Fred Graham (Essex)
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