There was little between the teams until referee Trevor Kettle ruled that Lincoln defender Paul Green fouled Chris Holroyd as the Chester player went up for a header.
There appeared to be no contact between the players, but despite Lincoln's protests, Green was yellow carded and Tony Dinning slotted home the spot-kick.
The 57th minute winner was harsh on Lincoln, who produced a passionate performance for new boss Peter Jackson.
The Imps were unlucky in the seventh minute when a cross from Gary Croft opened up the Chester defence.
Steve Torpey sent in header which beat keeper John Danby but the ball came back off the bar.
Croft blasted a 25-yard shot narrowly wide before Lincoln suffered a blow in the 29th minute when influential centre-back Lee Beevers was forced off with a dislocated shoulder.
Chester produced a rare attack in the 38th minute when Dinning fired in a shot from 35 yards but Lincoln keeper Alan Marriott produced a diving save.
Danny N'Guessan and Torpey both went close at the other end before the second-half penalty put Chester in the driving seat.
Lincoln became increasingly frustrated by the referee's decisions and were denied an equaliser in the 70th minute when Ben Wright forced the ball in from close range only to see his effort disallowed for an earlier foul.
N'Guessan was denied an equaliser 14 minutes from time when his superbly struck shot was well saved by Danby.
Chester arrived nearly an hour late for the game after their team coach was stuck in traffic on the A1 and now face a fine from the Football League.