A slow paced game was sparked into life during a frantic five-minute spell but Lucas Digne salvaged a point in the last minute of added time.
Richarlison opened the scoring with an emphatic finish after a pullback from Andre Gomes.
Watford equalised through a Seamus Coleman own goal which had been coming after Watford's pressure in the second half.
Within two minutes Watford had taken the lead through Abdoulaye Doucoure.
Unbelievably Everton got a penalty one minute later which Gylfi Sigurdsson saw saved by Foster.
With less than one minute to play, Christain Kabasele gave away a free kick that Digne dispatched fantastically.
Perfect start for Richarlison
Everton's first goal should have been ruled out for offside after Theo Walcott stopped the ball for Gomes to run onto despite the winger being clearly offside.
Once Gomes pulled the ball back for Richarlison there was no chance he was going to miss from less than 12-yards out.
Watford's best chance of the half was a header from Roberto Pereyra when he got between the two centre-backs but could only glance a free header wide of the post.
Everton almost doubled their lead just before the break when Sigurdsson played a neat one-two with Digne but he couldn't get the ball out his feet and had to settle for a corner.
Pereyra had another good chance for Watford in the second half from a free-kick that went through a gap in the wall and looked like it was in but the Argentine only found the side netting.
Mad five minutes
However, Watford's eventual equaliser came from their best player on the night, Preyra who flicked his shot onto the post but it came back out and rebounded off the Everton captain and into his own net.
That kick-started a frantic five minutes in which the away side took the lead after a smart quick free-kick was taken and Pereyra was involved again as he crossed for Doucoure to head home from a matter of yards.
Sigurdsson lets Everton down again from the spot
One minute later Kabasele gave away a penalty after fouling Yerry Mina and as Sigurdsson steps up to put the home side level again he tries to go down the middle but Foster saves brilliantly with his foot.
It looked perfectly set up for the pantomime villain Richarlison to grab his second of the game but after the ball, fortunately, fell to him less than six-yards out he tripped over his own feet and couldn't even get a shot away.
Digne the unlikely hero
When it looked like the Toffees had thrown away a leading position Kabasele gave away an unnecessary free-kick when he handled the ball just outside the area.
Digne stepped up with less than one minute left to play and placed it beautifully into the top corner to secure an unlikely point for the home side.
An exhilarating game that will have left both managers frustrated as both sides dominated for long periods of the game, Everton in the first half and Watford in the second half.