A late own goal saw Everton fall to a 2-1 defeat at Bournemouth after Beto's late strike looked to have rescued a point for the Blues at the Vitality Stadium.
The hosts took the lead just after the hour when Dominic Solanke headed home a cross from the left flank.
Beto stepped off the bench and looked to have rescued a point when he pounced on a goalkeeper error to convert from close range with just three minutes remaining.
But there would be late agony for the Toffees, as Adam Smith's speculative cross hit Seamus Coleman inside the six-yard box and ended up in the back of the net to leave Sean Dyche's men empty-handed at the end of a cagey contest.
Coleman and Dominic Calvert-Lewin were recalled to the starting line-up following a three-week break in the fixtures schedule, replacing Vitalii Mykolenko, who missed out on the matchday squad through illness, while Beto dropped to the bench.
The Blues have been far from passive guests on the road so far this campaign and had won all six away Premier League games against teams currently in the bottom half of the table heading into this clash.
After winning the coin toss and once again switching ends - a common theme on the road this term - Dyche's side started positively but it was Jordan Pickford who was called into action early on to deny Antoine Semenyo's drive from the edge of the penalty area. The rebound fell to Lewis Cook, whose half volley sailed comfortably over the target.
Everton's first meaningful response came after a counter-attack of their own, Amadou Onana finding Abdoulaye Doucouré, who did well to help the ball on to Calvert-Lewin inside a congested penalty area before the Blues' No.9 saw his goal-bound strike deflected behind for a corner.
The Toffees were shading the possession count and threatened twice in the space of three minutes just after the half-hour mark - Calvert-Lewin forcing Neto into a save at full stretch down before McNeil saw a low drive from the edge of the penalty area drift the wrong side of Neto's left-hand post with the Cherries goalkeeper rooted to the spot.
The closing chapter of a relatively quiet opening period nearly saw the hosts break the deadlock but, after appeals for a penalty were waved away by referee Sam Barrott, Semenyo's snap-shot cannoned back off the frame of the goal and away to safety.
Everton had genuine claims for a spot-kick of their own 10 minutes after the half-time interval but the contact made by Tyler Adams on Calvert-Lewin was deemed not enough for referee Barrott to present the Blues a chance from 12 yards.
A clever corner routine then saw the Toffees go close again. McNeil had initially played a short one-two with Harrison before skipping past his marker and delivering a cross that grazed the post before hitting a Bournemouth defender and bouncing agonisingly wide of the target.
Bournemouth opened the scoring on 64 minutes, as top scorer Dominic Solanke got between two defenders and nodded home substitute Lloyd Kelly's centre.
Dyche shuffled his pack in a bid to restore parity with a double substitution that saw Andre Gomes and Ashley Young introduced, then Beto introduced in place of Amadou Onana.
It was the Portuguese striker who would get Everton back on level terms with three minutes remaining, slotting home from close range after Neto had dropped McNeil's cross following a collision with teammate Chris Mepham.
But there would be late drama that would see the hosts snatch all three points, when Smith's cross from the right wing bounced inside Everton's six-yard box, hit Coleman and ended up in the back of the net.
Everton now face a quick turnaround with a trip to Newcastle United on Tuesday evening.
