The talented youngster found himself in space two minutes into time added on as he took a cross from Andy Holt and drilled a low shot past City keeper Alan Marriott.
Lincoln were under pressure early on but they had three great chances, two from Wrexham back passes and the other from a free-kick that went wrong.
Simon Yeo put them in front just after the hour, but he missed two golden chances earlier before making amends.
Firstly he should have scored when a Dave Bayliss back-pass put him through with only goalkeeper Mike Ingham in his way, but his wayward shot curled past the post with the keeper beaten.
He then missed a great opening when a back-pass from Dennis Lawrence left Ingham stranded but Yeo stabbed out a foot and missed the ball completely in front of a gaping net, allowing time for the home keeper to scramble across his line and make a vital save.
When the goal arrived it came via a through ball by Colin Cryan which was intended for Scott Kerr, who missed the ball in the six-yard box where it skidded through for a surprised Yeo to turn it in at the far post.
City made a quick substitution after seeing Wrexham's line up, withdrawing Paul Mayo and sending on the lofty Nathaniel Brown to give more height up front.
They had an early opening when Francis Green crossed and Yeo came in at the near post where Ingham dived to take the ball off his toes.
At the other end Mark Jones aimed a free-kick wide before Dean Bennett saw a crisp shot turned for a corner. From another cross by Danny Williams, Marriott went full stretch to collect as Jon Walters came in.
Lincoln gained in confidence in the second half and went close when Dean Keates crossed from the left to set up Green who just missed contact at the far post.
Keates was too close for Wrexham's comfort with a 20-yard drive that Ingham did well to stop.
With City ahead and beginning to take control Wrexham made a double substitution bringing on Robbie Foy and youngster Jamie Read as extra attackers but they made little headway.
Bayliss saw a shot saved in a crowded goal mouth before Jones finally broke through to put the home side level.