York City took the lead 28 minutes into this Isuzu FA Trophy Fourth Round tie, as Olly Dyson, returning from illness, headed in from Alex Hurst's cross.
The reply from lower-league Chelmsford City took eight minutes to arrive, the wind playing a huge part in Eduino Vaz's looping cross-shot, which left goalkeeper Ethan Ross with no chance.
The second half saw chances aplenty for the Minstermen, but they failed to make them count, as the game headed for a penalty shoot-out.
York held a 100% record through all five spot-kicks, while experienced Clarets striker Simeon Jackson paid the price for his tame strike from 12 yards.
It was well kept out by Ethan Ross to help send the Yorkshire side through to the round of 16, winning 5-4 on penalties.
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Story of the match
With focus switching from the National League to the FA Trophy for York City, manager David Webb made use of squad rotation, making six changes to the side which had beaten Maidstone a week earlier.
Following on from Chelmsford's National League South defeat to Chippenham, boss Robbie Simpson brought new goalkeeper Eddie Beach straight into the lineup, in one of three changes made.
The cup tie underwent a quiet opening ten minutes, as York controlled most of the possession, but it was the lower-league visitors that struck the first attempt of the game, with Harry Lodovica driving it wide of goal from an angle.
Another opportunity to open the scoring came the Clarets' way on 14 minutes, yet shooting range was narrowed by a couple of defenders, and Callum Jones couldn't do much more than roll it well wide from 15 yards.
Minutes later, the Minstermen awakened; a good move finally resulted in a chance.
A beautiful through ball from last week's hat-trick hero Shaqai Forde was latched onto by striking partner Manny Duku, but he took one touch too many, allowing Chelmsford 'keeper Beach to rush off his line and block the eventual effort.
Soon enough, the breakthrough goal came. An Alex Hurst cross in from the left found a patiently waiting Olly Dyson at the back post, making no mistake to nod home and give the hosts a lead two minutes short of the half hour mark.
Eight minutes on from the opener came a leveler, which sent David Webb's game plans back to square one again.
The blustery conditions could quite possibly have intervened in Eduino Vaz's cross-cum-shot from the edge of the area on the left, but it was of no care to the youngster, who watched the ball sail into the far corner, grabbing his first ever goal in senior football, and one which brought the Essex side back on terms.
In an attempt to restore the advantage, midfielder Dan Pybus linked up with Forde, before the latter tried a low shot from 20 yards, only to have it turned around the post by Beach.
A scrappy end to the first half saw a burst from Nathan Thomas into the Chelmsford box, but Beach was there once again to deny the Minstermen winger with an outstretched leg, before moments later, he blasted over from a similar point inside the area.
Frustrated by a Clarets side that sat fourth in their division, the Yorkshire outfit weren't likely to be content with being held at the interval.
The aim was to regain the lead early in the half, and they were merely inches away from doing that.
After Adam Crookes had failed to advance far enough into the box, the ball was laid off to fellow half-time substitute Mitch Hancox, who almost lofted a cross-shot into the top right corner, though it was the woodwork that saved the 'keeper from some embarrassment.
Forde was yet to get on the scoresheet for the hosts in this game following four goals in his two previous matches, but even when presented with a glaring opportunity, he still couldn't find the net.
A ball in behind the Chelmsford defence was ran onto by the York forward, and with only the goalkeeper to beat, an attempted dink just didn't have enough height on it to take it over the stopper, who caught easily.
With a free kick awarded to the visitors 19 minutes into the second 45, it was goalscorer Vaz who stepped up, dreaming of giving his side a shock lead, but it wasn't to be this time, as he watched his set-piece lift over the wall, and narrowly evade the right-hand post.
Barely a minute later, down at the opposite end, a ball into the mixer was headed out, only as far as loanee Forde, who struck a brilliant half-volley with venom destined for goal, albeit a deflection prevented it, directing it onto the crossbar and out for a corner, which, in time, was headed over by Fraser Kerr.
The chances kept on coming for the Minstermen, and it was that man Forde once again, curling one over from range, before Thomas' break into the box shortly after concluded in him striking the wrong side of the post.
Despite the constant threat from York, the Wembley dream was still very much alive for Chelmsford - a couple of rare attacking moves gave them hope, but alike their opponents, they failed to convert.
Potentially the best chance that they would get came right at the very death, with Simeon Jackson's through ball finding Liam Trotter in a one-on-one with 'keeper Ethan Ross, but injuring himself in the process, Trotter's hopeful effort was excellently blocked by the stand-in captain.
A penalty shoot-out it was to be, after neither side could be separated after 90 minutes - it would be the first ever at the LNER Community Stadium.
York Penalty Perfection
Referee Michael Barlow had carried out the coin toss, and it was arranged that Chelmsford would step up first, though to be taken right in front of the masses of York City fans.
Kai Yearn was first up for the visitors, sending the 'keeper the wrong way to give his side the start they needed.
He was followed by York's Thomas, who also managed to put his spot-kick away.
Former-Premier League striker Jackson was next up to take, and with bags of experience on his side, chose right, and agonizingly watched his penalty palmed clear by Ross.
Hancox was calm and collected in firing down the middle for the Minstermen; the Clarets' Jamie Yila followed suit in netting his penalty, squeezing it into the corner.
The next two takers in Hurst and Jones made no mistake in hitting the back of the net, to bring tension around the stadium, the final few spot-kicks edging closer.
York took the lead again, with Pybus' stuttered run-up eventually finding the top corner.
Cameron James avoided a miss to keep Chelmsford in the tie, but it was in the hands of the Minstermen's goalscorer Dyson to decide the fate of this penalty shoot-out.
Dyson stepped up and delivered for the hosts, to dump the Clarets out of the competition, and secure York City a place in the Fifth Round.
The draw for the Isuzu FA Trophy takes place on Monday at 3pm.
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Player of the match
Olly Dyson (York City)