Steven Naismith netted for the fourth time this season but Everton were beaten 2-1 by Manchester United.
The Blues went down fighting at Old Trafford and it took a man of the match performance from goalkeeper David De Gea to deny the spirited Toffees at least a point.
Angel Di Maria put United ahead midway through the first half before De Gea denied Leighton Baines from the spot on the stroke of half-time – ending the left-back’s 100 per cent Premier League penalty record for the Club.
Naismith headed the Blues back level 10 minutes into the second period before Radamel Falcao netted the game’s decisive third goal.
Everton launched a late onslaught but they came up against a stubborn De Gea who produced two saves of the highest order to thwart substitutes Leon Osman and Bryan Oviedo in stoppage time.
Worryingly for the Toffees, John Stones was stretched off in the dying seconds after appearing to roll his ankle having advanced forward to attack a corner.
Everton were on the back-foot for most of the first half and had to weather a lot of early pressure from Manchester United.
Falcao tested Howard with a diving header inside the opening five minutes before Di Maria delivered an inviting cross for Robin van Persie who fired over at the near post.
Di Maria’s influence in the game continued to grow as the first half progressed and it was the Argentinian playmaker who opened the scoring on 27 minutes.
Juan Mata teed-up the former Real Madrid man just inside the area and a perfectly-placed right-footed curler found the corner of the net.
Di Maria nearly had his second moments later but this time Howard was equal to his 30-yard free-kick, pushing it behind for a corner.
The Blues’ response to falling behind was positive though and Romelu Lukaku – one of four changes to the team that drew at Krasnodar – volleyed wide from a tight angle after latching on to a ball down the left channel from Leighton Baines.
Then, on the stroke of half-time, Tony Hibbert powered into the Manchester United box and went to ground under a Luke Shaw challenge. Referee Kevin Friend pointed to the spot but De Gea guessed correctly, dove to his right and beat away Baines’ penalty.
The Everton left-back did not let that disappointment affect his performance in any way and 10 minutes into the second half it was the England man who delivered an inch-perfect cross for Naismith’s equaliser.
Baines and Barry played a crisp one-two from a quickly-taken free-kick and the Scotland striker ghosted in at the far post to nod the Blues back level in front of the Stretford End.
Everton had their tails up and Phil Jagielka almost bagged his second goal in as many Premier League games in the next attack – only to be denied by Falcao who made a vital goalline clearance.
The Colombian’s game is all about instinct and just two minutes later he again pounced – this time at the opposite end of the pitch to put the home side back level.
Di Maria scuffed a shot from outside the box and Falcao stuck out a boot to divert the ball past Howard. The Everton defence claimed for offside but replays showed the loan signing from Monaco was just level.
Oviedo – back at the scene of his most famous moment in an Everton shirt - was sent on from the bench by Martinez, as too was Osman.
It was all Everton in the final stages and it took two world-class saves from De Gea to deny the both aforementioned substitutes equalisers deep into the stoppage time.
The Spaniard thrust out a right arm to deny Osman before making an even better stop to turn Oviedo’s 20-yard half-volley over the bar.
But, unlike the two previous games against Liverpool and FC Krasnodar, there was to be no late leveller for the battling Blues.