Trailing 2-0 to a pair of second-half goals, Everton battled from behind and dramatically piled on three match-turning goals to move out of the relegation zone with a first victory in five Premier League matches.
Their incredible fightback almost took a heartbreaking twist when Watford were awarded a spot-kick in the 11th added minute, injuries to Heurelho Gomes and Christian Kabasele causing lengthy stoppages, but former Toffee Cleverley drilled his spot-kick wide as the hosts escaped with a potentially season-turning triumph.
Amid reports Sean Dyche is set to take over, Everton looked destined for defeat as they trailed by two goals until the 67th minute. Richarlison made up for a first-half miss by opening the scoring less than a minute into the second half, before Kabasele – who was later taken off on a stretcher – headed the visitors further ahead.
Oumar Niasse provided the Toffees a lifeline by punishing a Watford lapse at the back and substitute Dominic Calvert-Lewin made it two in seven minutes when he nodded in from a corner, setting up a tense finale.
Few would have predicted what followed. Everton were rewarded for their endeavour as Leighton Baines dispatched a penalty in the 91st minute, before Cleverley's miss at the other end gifted David Unsworth a memorable first win in what could be his final match as caretaker manager.
Teenage midfielder Beni Baningime, in his first Premier League start, and a fit-again Michael Keane made important interceptions to see off an early spell of Watford pressure and set the platform for the game's first chance – Baines hitting a meek finish straight at Gomes.
Richarlison also wasted a chance for the opener when he hit the side-netting after rounding Jordan Pickford, although the Brazilian made no mistake when presented with a similar chance just 30 seconds after the interval, firing in at close-range after Andre Gray's smart pass unlocked a scrambled Everton defence.
The hosts should have drawn level less than 10 minutes later when Niasse teed up for Gylfi Sigurdsson for a seemingly certain goal, but Gomes stuck out a hand to divert his effort.
The goalkeeper's heroics came to a premature end as Niasse's knee inadvertently collided with his head and forced Marco Silva to turn to back-up goalkeeper Orestis Karnezis.
Watford were jubilant again when Kabasele headed in Jose Holebas' corner to extend the margin just after the hour, although their two-goal buffer lasted only three minutes.
Niasse stole in between Holebas and the onrushing Karnezis and did enough to force the ball into an empty net.
And the Toffees' comeback took on new life through Calvert-Lewin, who replaced Wayne Rooney and nodded in a corner at the far post for his side's second.
Watford's disappointment was compounded when Kabasele was forced off following a collision with Pickford, and Silva's anguish only grew in added time.
Holebas tripped substitute Aaron Lennon inside the area, enabling Baines to atone for his first half miss with a cool penalty into the bottom left corner which appeared to have put the seal on a breathless come-from-behind victory.
Unsworth's side did escape with three much-needed points as Cleverley failed to match Baines' calm, firing wide of the left upright in the 11th minute of stoppage time after Pickford's foul on Richarlison sent the midfielder to the spot.
Key Opta stats:
- Everton came from two goals down to win at home in the Premier League for only the second time ever and for the first time since May 1994 v Wimbledon (3-2).
- Richarlison has been directly involved in six goals in the Premier League this season (4 goals, 2 assists), more than any other Watford player.
- Oumar Niasse has netted four goals in his four Premier League appearances at Goodison Park for Everton this season.
- Dominic Calvert-Lewin has had a hand in more goals in all comps this term than any other Everton player (5 goals, 2 assists).
- Leighton Baines scored and assisted in the same Premier League game for only the third time ever and for the first time since November 2011 (v Wolves).