Aidy Boothroyd's side served up a shocker the last time they were on live television, coincidentally against the red half of Merseyside, but there was no sign that the stage fright has been cured during a woeful opening 45 minutes that saw Manuel Fernandes score before Andy Johnson netted another penalty he was controversially awarded.
Indeed, the Toffees should have been four goals to the good by the break, but Tim Cahill and James Beattie failed to convert chances that looked easier to score than miss.
The beleaguered Hornets did briefly threaten a revival after the break, with substitute Tamas Priskin going close on three occasions, but Leon Osman applied the gloss in injury-time with a delightful 20-yard shot.
Watford, with the incentive of knowing three points would take them off the bottom of the table for the first time in three months, started marginally the better before they almost gifted Everton the lead and then found themselves firmly up against it midway through the first half.
Richard Lee, playing because of the injury sustained by Ben Foster in the 1-1 draw with Wigan, was almost left red-faced when he let a 19th minute drive from Cahill squirm through his grasp, but he managed to dive on the ball as it rolled towards his net.
The Hornets keeper then redeemed himself with a spring-heeled leap to turn behind Johnson's deft header from a Cahill cross moments later, but the visitors then took firm control.
Everton's opener arose after they broke forward at pace and Mikel Arteta cut in from the right before sliding the ball across the area to Cahill, and he struck a first time right-footed shot that bounced up in front of Lee.
The keeper could only parry back in the direction of Johnson and Manuel Fernandes in the heart of the penalty area and the latter was adjudged to have converted the rebound via the underside of Jay DeMerit's leg, although it looked as if Johnson may have got the decisive touch.
As Watford sought to recover from that setback, they found themselves two down in next to no time.
It looked a case of six of one, half a dozen of the other in the pushing and pulling stakes as Johnson just got goalside of Adrian Mariappa as he attacked the left side of the area and went down, but referee Lee Mason immediately pointed to the spot and the former Crystal Palace striker slammed the penalty down the middle of the goal to make it 2-0.
But how two didn't become three moments later, only Cahill will know. The Australian was picked out in the heart of the area by Lee Carsley's ball over the top of a statuesque Hornets defence, but with just Lee to beat the midfielder lifted the ball over the target.
Watford managed to quell the Everton tide for a period, but the visitors should still have been three up by the interval.
DeMerit seemed to have down the hard work when he showed Johnson away from goal as he sought to latch on to a ball over the top, only to badly mis-control and let the forward lay a straightforward opportunity on a plate for James Beattie, but the striker replicated Cahill's previous miss and blazed horribly over.
Not surprisingly, Boothroyd reshuffled his beleaguered troops at half-time and one of the substitutes, Priskin, almost produced a single-handed fightback with three fine efforts in the space of six minutes.
First, he sent a 25-yard drive inches wide of Tim Howard's far post, then he also beat the American and the same upright with a diving header from a Steve Kabba cross, before heading down and wide of the keeper's right-hand upright again from a Tommy Smith centre.
But that was as good as it got for the Hornets and Arteta was unfortunate to see a goal-bound drive deflected behind by Jordan Stewart, before Osman put the icing on a winning cake late on.