Michael Ingham was beaten at his near post by Enver-Marum
Liam Enver-Marum scored the only goal as Eastbourne stunned promotion-chasing York City, ending their 10-month unbeaten home record in the process.
The 10-goal striker beat defenders Luke Graham and James Meredith and fired home at Michael Ingham's near post.
The goal came against the run of play, although City had failed to create many clear-cut chances beforehand.
Richard Paquette had chances to level, but volleyed against the crossbar and fired across goal late on.
City's last home defeat came on 11 April 2009, a 2-1 reverse against Northwich, and Borough had won just two of their away games in the league this season.
The victory moves Borough two points clear of the relegation zone and leaves York nine points behind leaders Oxford United, having played a game more.
York's best chance in the first half came when David McGurk connected to a right-wing cross, but he was stretching and put it wide.
Pacquette could have put them ahead moments after stepping off the bench but he fired over the bar and he was made to pay when Enver-Marum fired home.
The former Woking striker had a chance to double the visitors' lead, when Ingham spilled his shot from 20 yards out but they held out for a shock win.
Pacquette had two chances late on and McGurk headed over with moments remaining.
Eastbourne manager Garry Wilson told BBC Sussex: "We always knew it was going to be difficult and the task was enormous.
"We said to all the players that each and every player would need to have their levels up. I thought we lifted our game and really came together as a team.
"We held on well and our keeper was never really under any pressure. This is a real platform for build on for us. We'll focus on Stevenage now."
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