They should have added a second five minutes later but Dave Cameron shot wide from the edge of the box with just Glennon to beat.
Jan Molby decided to substitute the two wingers - Rob Matthews and Ryan Williams - bringing on Lawrie Dudfield and Ben Petty in the 26th minute.
Minutes before half time Dudfield set up a great opportunity for strike partner Gary Alexander. He cut the ball back from the left, but Alexander with the free shot failed to beat keeper Alan Marriott.
Dudfield showed him how to do it in the 45th minute, when Ben Morley's pinpoint left-footed cross from the right was headed into the bottom corner of Marriott's goal to make it 1-1 at half time.
At the start of the second half Dudfield did well with a volley, after Petty had spooned it, but it went wide.
20 minutes from time Lee Philpott should have scored against his former team. Beresford crossed from the right to Philpott who saw his shot parried out by Marriott, and then hit a wayward right-footed rebound well off target.
Both sides had great chances in the closing stages. Holt's cross to Alexander was blasted against the underside of the bar, and then cleared by the defender on the line. It had looked to have gone in, and Alexander was booked for arguing that he should have been awarded his 24th goal of the season.
Lincoln then went up the other end of the pitch and Battersby put the ball across the face of goal from the right, but David Cameron from just a few yards out scuffed the shot and put it wide under pressure from Morley.
City line-up (4-4-2): Glennon; Morley, Greaves, Mohan, Edwards; Williams (Dudfield), Johnsson, Philpott (Holt), Matthews (Petty); Alexander, Beresford.
Un-used subs: Musselwhite, Whittle.