Swiss midfielder Abdi and Czech striker Vydra, both on loan with the Hornets from Udinese - the Italian club also owned by Vicarage Road bosses, the Pozzo family - found the net in the last three minutes to sink a Palace side who had led for the best part of an hour.
Owen Garvan had twice put the hosts ahead in the first half with Martin Taylor equalising for Watford.
But Abdi levelled again with a 25-yard strike before Vydra sent the visiting fans wild with the winner deep into stoppage time.
Zola's side created the first chance with Joe Garner planting an early header wide before Abdi shot straight at Julian Speroni.
But Palace went ahead after 13 minutes when Hornets skipper John Eustace brought down Wilfried Zaha in the area.
Referee Andy D'Urso had no hesitation in pointing to the spot and Garvan coolly found the top corner.
Watford attempted to hit straight back with Garner's header clipping the bar and a deflection sending Mark Yeates' shot wide.
And they got their equaliser in the 22nd minute when Palace failed to clear a corner from Carl Dickinson.
Sean Murray blasted the loose ball back towards goal and Speroni spilled it at the feet of Taylor, who had the simple task of tapping it into the net.
But Palace got their noses back in front just seven minutes later, Garvan controlling a flick-on from Speroni's goal-kick on his chest before lashing the ball past former Arsenal keeper Manuel Almunia.
The Eagles could have been two ahead before half-time but Taylor cleared a header from Kagisho Dikgacoi off the line.
After the interval Dickinson's free-kick found Eustace in the area but the midfielder skied his effort.
Murray also fired over from long range and Dickinson's shot flew wide.
Palace also had their chances after the break, with Mile Jedinak heading Garvan's corner over the top.
Zola threw on big striker Chris Iwelumo, who climbed off the bench to hit the winner against Wycombe in the Capital One Cup last weekend, with 12 minutes to go.
But it was Abdi who sparked the comeback with a superb long-range strike after collecting the ball from Vydra.
And with virtually the last kick of the game Vydra latched on to Dickinson's pass and fired past Speroni from outside the box.