Lincoln had the better of the opening exchanges and N'Guessan was soon in the thick of the action when he forced home keeper Joe Anyon to make an early save.
Vale, now beaten nine times at home in the league this season, were showing no belief at all and it was no surprise when the visitors took a 12th-minute lead.
Scott Kerr's curling left-wing corner came back off the far post after striking a defender's head and N'Guessan got the final touch in a crowded six-yard box.
Vale did show some spirit after that and Kyle Perry was close to a 25th-minute equaliser when his header from Paul Edwards' cross was tipped over by Rob Burch.
But Lincoln were always a threat at set-plays and were inches away from a second when Lee Beevers headed a Stefan Oakes corner narrowly over the top.
The homes fans were showing no sympathy as cries of "what a load of rubbish" and "what a waste of money" tumbled from the stands.
Vale were then booed from the field at half-time and there was little sign of any improvement at the start of the second period.
A decent chance finally came their way in the 53rd minute when teenager James Lawrie miscued his shot after a driving run from Lee Collins.
But the visitors hit back as N'Guessan's blistering drive was well saved by Anyon and Lenell John-Lewis' header was ruled out for an infringement.
Vale boss Dean Glover's decision to replace striker Perry with centre-back John McCombe drew further derision from the home supporters.
However, Lincoln were not seriously troubled until McCombe twice went close in the last few minutes.