Ford's double gave 10-man Killie their first derby win since 1994 in the fourth-round replay at Rugby Park.
Bryan Prunty controversially put the Scottish Second Division side ahead in the 10th minute of an enthralling tie when he appeared to use a hand to knock the ball past Killie keeper Alan Combe.
When Ford headed the equaliser four minutes after the break - his first of the season - it looked like there would only be one winner.
But Killie striker David Fernandez was then shown a straight red card for appearing to strike Ayr defender Martyn Campbell, which gave the Honest Men another lease of life.
However, Mehdi Taouil put the home side into the lead before Ford added a third with another header to send the Killie fans home in raptures.
The match lived up to the first game, which had ended 2-2 at Somerset Park.
It began in a whirlwind fashion and in the fifth minute, as supporters continued to flood in, Ayr defender Neil McGowan brilliantly headed clear a Willie Gibson cross off the line with Killie midfielder Craig Bryson ready to bundle the ball over the line.
But in the 10th minute the game turned on its head when the visitors stole into the lead with a controversial goal.
A long ball from Dean Keenan had Prunty on the chase with Ford and, when Combe came racing out to the edge of the box, the Ayr striker appeared to knock the ball past both of them with his hand.
The goal seemed to immediately drain Killie of all confidence and for the next few minutes the home players were clearly rattled, although a run and shot by Willie Gibson, which narrowly missed the post, provided some hope for the home fans.
Killie stepped up the pace and in the ensuing mayhem that characterised the search for an equaliser, Prunty went off injured to be replaced by Alex Williams, United's hero from the first game.
An inswinging free-kick from Gibson had Ayr keeper Stephen Grindlay flying into a packed six-yard box to clear for a corner and moments later an even better delivery from the Killie wide-man caused more panic but the Second Division side again emerged unscathed.
Killie, with almost total possession, continued to pepper the visitors' box with crosses but to no avail. In the 34th minute Ford moved forward to try his luck from 30 yards but the ball trundled wide of the target to the delight of the 4,000 Ayr fans behind the goal.
In the 39th minute, during another goalmouth melee, McGowan again cleared off the line, this time from Rugby Park striker Allan Russell, who had tried to squeeze the ball in at the post.
An exhilarating first 45 minutes ended with Killie still on top and the home fans were less than enamoured as news spread around the stadium that Prunty had admitted on television at the break he had, indeed, handled for the goal.
The home side won a corner with less than 30 seconds gone in the second half to signal their intent and in the 49th minute, after Russell was fouled by William Easton 35 yards out, they were deservedly level.
When Gibson floated the free-kick over to the back post, Ford rose among a posse of players to send in a header that proved too powerful for Grindlay to stop going over the line, although it looked like the Ayr keeper might have made a better effort.
At times Killie were camped outside the Second Division side's box and in the 65th minute Grindlay made a superb block from Ford's close-range header, which came after Gibson had again floated a cross into the Ayr box.
In the 68th minute Killie were reduced to 10 men when Fernandez clashed with Campbell at the corner flag, the Killie striker appearing to slap his opponent.
The red card galvanised the visitors and moments later Combe had to make a save from David Gormley after an Ayr counter.
But in the 75th minute Killie eventually forged ahead after fine play by Bryson.
The Killie midfielder slalomed into the Ayr box past three defenders and, when his drive was blocked by Grindlay, Taouil slammed the rebound in off the post.
More drama was to follow 10 minutes from time when Ford sealed the trip to Inverness in the next round when he glanced in a Taouil corner.