Ebbsfleet won away for the first time this season despite having goalkeeper Preston Edwards sent-off.
Edwards saw red for handling the ball outside the box with just over half-an-hour played at York Road on Saturday.
The score was 0-0 at that stage but Charlie Sheringham put Ebbsfleet in front just before the interval and the 10 men produced a great rearguard action in the second period.
Anthony Cook's late goal rounded off an excellent day for the north Kent club.
There were three changes to the Ebbsfleet side following their 3-2 defeat at Weston-super-Mare in midweek. Aiden Palmer was recalled in defence, taking the place of Shane Huke, while in midfield, Alex Osborn and Matt Johnson came in for Matty Godden and Tommy Fraser.
Gary MacDonald, who was part of Ebbsfleet's 2008 FA Trophy-winning side, lined up in defence for the home side.
Hayes went straight on the attack and put Steve Brown's men under early pressure. Miscommunication in the Fleet defence almost let Matt Ruby in for a tap-in when the visitors failed to deal with a corner - but they finally scrambled the ball clear.
Osborn cut in from the right wing and dragged a left-footed shot wide at the other end, but Ebbsfleet too often resorted to hopeful balls out of defence, which gave strikers Sheringham and Billy Bricknell precious little to feed off.
Hayes skipper Matty Harriott suddenly found himself free in the Ebbsfleet penalty area but Edwards pulled off a vital save with his foot.
With 32 minutes played, though Edwards' afternoon came to a premature end. He rushed to the edge of his box to collect a high ball but lost his bearings and caught it just outside the area. Referee Savva Yianni, after consulting with his assistant, pulled out the red card.
Bricknell was sacrificed so reserve keeper Brandon Hall could go in goal.
Hall, a former Hayes & Yeading player, was almost beaten within a minute of coming on. MacDonald's free-kick deflected just past the post and from the resulting corner, Dean Inman powered a header over the bar.
But, against the run of play, Ebbsfleet took the lead a minute before half-time. Osborn drove towards the Hayes area and slipped the ball right into the path of Sheringham, who arrowed a precise shot across Calum Kitscha and into the far corner.
Hayes made a change at the start of the second half, bringing on Rhys Murrell-Williamson for MacDonald. The substitute was involved straight away, setting up Harriott for a shot which sailed over. Dan Wishart then got free on the left but smashed his shot well wide.
But the visitors almost scored a bizarre equaliser when Anthony Acheampong's back-pass sold Hall short and the goalkeeper's attempted clearance hit Louis-Rae Beadle, bouncing wide.
Osborn, having been fouled moments earlier, went down injured just outside the Hayes box after seeing a shot charged down. He limped off the field and Godden took his place on the right wing.
Cliff Akurang, who gave Ebbsfleet so many problems in Bishop's Stortford colours last season, came on for his Hayes debut and almost scored with his first touch. Hall, though, got down well to grab a cross from the left.
At the other end, Cook dummied Godden's right-wing cross, intending the ball to run into Sheringham's path, but Hayes intercepted and cleared.
Hall and his defenders dealt well with the high balls which Hayes swung into the box but the goalkeeper was totally beaten by a Harriott strike from 25 yards, following a quick free-kick. Harriott's shot looked to be creeping in but it hit the post and bounced behind.
How fine the margins can be in football.
Moments later, Cook doubled the Fleet's lead, nutmegging Adam Everitt and smashing the ball past Kitscha to the delight of the travelling fans.
Harriott went close again following the restart, unloading from 30 yards, only to see Hall spring high to his right to claw the ball out of the top corner. Pat Cox was booked for punching the ball in from Hayes & Yeading's next attack - and Akurang headed a left-wing cross over.
It was almost 3-0 when Cook won the ball in the left-hand corner and, ignoring Sheringham's shouts for a pass, cut inside and forced an excellent save from Kitscha.
Harriott took aim again in stoppage-time but Hall - and Ebbsfleet - stood firm.
Hayes & Yeading: Kitshca, Vanderhyde (Anyinsah 77mins), Everitt, MacDonald (Murrell-Williamson 46mins), Ruby, Inman, Ijaha, Harriott, Cox, Beadle (Akurang 62mins), Wishart. Subs not used: Merrifield, Smith.
Ebbsfleet: Edwards, Howe, Acheampong, Clark, Palmer, Osborn (Godden 58mins), M Johnson, Rance, Cook (C Johnson 90mins), Sheringham, Bricknell (Hall 33mins). Subs not used: Huke, Fraser.