EPL PHOTOS: Liverpool and United thwarted in dramatic finales

Premier League heavyweights Liverpool and Manchester United were caught by late sucker punches in two games that finished far more dramatically than they began on Sunday.

Juergen Klopp's Liverpool wasted a chance to return to second place in the table, a point behind Chelsea, twice surrendering a two-goal lead before losing 4-3 in added time in a thriller at Bournemouth.

United dropped two points at Everton after Marouane Fellaini conceded an 89th-minute penalty soon after the former GoodisonPark favourite had come on as a substitute.

Third-placed Liverpool's defeat was their first in any competition since August and looked highly improbable when they built on a slow start to cruise into a 2-0 lead midway through the first half.

Sadio Mane and Divock Origi, starting his first league game of the season, scored for the visitors from successive attacks.

Although Bournemouth had strong claims for a penalty turned down as Roberto Firmino challenged Nathan Ake, they did not threaten until the introduction of Scotland Under-21 international Ryan Fraser 10 minutes after halftime.

He had been on for barely a minute when he won a penalty that Callum Wilson converted.

Emre Can restored Liverpool's two-goal cushion but they were stunned when, in the space of three minutes, Fraser drove in Wilson's centre and then defender Steve Cook brought down Fraser's cross like a striker before driving home the equaliser.

In the third minute of added time Bournemouth secured one of the best wins in their history -- and first against Liverpool -- as goalkeeper Loris Karius fumbled a shot from long range and Ake poked the ball in.

Bournemouth manager Eddie Howe said it was "a very special day" for his 10th-placed team.

"It would have been easy for our players to give up and see out time but our group knows not to give up," he added.

Klopp said his side gave the points away although he was surprisingly sanguine about the outcome.

"Of course this can help us," the Liverpool manager explained. "If we learn, then it's OK.

"No road is without rocks and stones. It's three points, no more, these things happen. The base is pretty good but we need to use our quality more."

United manager Jose Mourinho also tried to dwell on the positives after he had sent on Fellaini against eighth-placed Everton.

The Belgian produced a clumsy tackle on Idrissa Gueye and could only watch as defender Leighton Baines beat the previously defiant David De Gea from the penalty spot.

Earlier, Zlatan Ibrahimovic continued his run of goals for sixth-placed United with a clever lob via the bar and post as goalkeeper Maarten Stekelenburg unwisely rushed out of the penalty area.

"We are not getting what we deserve," said Mourinho.

"In every one of our draws we deserved to win.

"You have (other) teams playing defensive and counter-attacking football but getting results.

"I'm happy my team is playing extremely well. But this season what matters is the results."

With six draws in the last eight league games and only one victory, results are not going United's way, leaving them nine points behind ManchesterCity who are in fourth spot.