Ole Gunnar Solskjaer's side were denied in heartbreaking fashion at Goodison Park having looked set for a point after equalising Gerard Deulofeu's openerSeamus Coleman's stoppage-time strike gave Everton a seventh consecutive home win as struggling Cardiff City were beaten 2-1.
The Republic of Ireland defender's sliced shot deep into stoppage time stunned Ole Gunnar Solskjaer's relegation-threatened side, who have now suffered eight consecutive away defeats.
Juan Cala's first goal for Cardiff looked to have secured a precious point in their battle to avoid the drop after fellow Spaniard Gerard Deulofeu had put Roberto Martinez's side in front.
But Coleman had the final say as Everton moved above Manchester United into sixth place in the Premier League and inflicted yet another defeat on a Cardiff side who nevertheless showed plenty of fighting spirit as goalkeeper David Marshall produced a string of outstanding saves.
|BATTLE AT THE BOTTOM
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Cala recovered from illness to take his place in the Cardiff side as Kenwyne Jones dropped to the bench and Kevin Theophile-Catherine replaced the injured Ben Turner in defence.
Kevin Mirallas must have thought he had put Everton ahead after just two minutes when he picked his spot with a measured right-footed strike, but Marshall produced a fine reflex save.
The tricky Deulofeu then went down in the penalty area under a challenge from fellow Spaniard Cala, but referee Roger East waved play on 22 minutes in.
Fraizer Campbell spurned a chance to open the scoring against the run of play six minutes later, as the alert Howard saved with his feet.
Marshall was delivering a goalkeeping masterclass at the other end as he thwarted Deulofeu and then produced an outstanding fingertip save to keep out Romelu Lukaku's venomous left-footed strike as the first half finished goalless.
Cala was in the thick of the action and the defender made a vital last-ditch challenge as Lukaku prepared to pull the trigger just after the break.
Everton were in front after 59 minutes though, and it was Deulofeu who got the breakthrough when he cut in from the left unchallenged and beat Marshall at his near post with a deflected effort.
Cardiff refused to lie down and they were level nine minutes later, when substitute Peter Whittingham whipped in an inviting free-kick which struck Cala and bounced down into the corner of the net.
The equaliser stunned Everton, but Osman almost restored their advantage when his vicious strike flashed just wide with Marshall beaten, before the goalkeeper produced yet more heroics to somehow tip Lukaku's deflected right-footed strike wide 12 minutes from time.
But Coleman won it right at the end with a scuffed effort that looped into the net after Gareth Barry had headed Aiden McGeady's cross into his path.