1 Liverpool 36
2 Man City 35
3 Arsenal 35
4 Everton 34
5 Chelsea 33
6 Newcastle 30
7 Tottenham 30
8 Man Utd 28
9 Southampton 24
10 Stoke City 21
11 Swansea 20
12 Hull City 20
13 A Villa 19
14 Norwich 19
15 Cardiff 17
16 West Brom 16
17 West Ham 14
18 C Palace 13
19 Fulham 13
20 Sunderland 10
A fierce strike from Seamus Coleman had given the visitors a 66th-minute lead with a ferocious strike, but they were pegged back when Bryan Oviedo put Dwight Tiendalli's off-target effort into his own net.
But Everton were not to be denied as midfielder Barkley stepped up with six minutes to go to beat Gerhard Tremmel with a strike which nicked the underside of the bar on its way in.
The goal, and another fine individual performance, will ensure the 20-year-old will again be in the headlines after a string of excellent recent displays, and it is hard to see how Roy Hodgson can leave him out of England's World Cup squad.
The win moves Everton up to fourth in the Barclays Premier League table, just two points behind leaders Arsenal, who play Chelsea on Monday night.
Earlier, Emmanuel Adebayor scored a brace as Tottenham claimed a 3-2 victory at Southampton that will only boost Tim Sherwood's chances of keeping the Tottenham job permanently.
Southampton opened the scoring after 13 minutes. Adam Lallana was allowed time and space on the edge of the Tottenham penalty area and found the bottom corner expertly.
The home side then threatened to run away with the game but Tottenham hit back when Roberto Soldado picked out Adebayor beautifully and the striker made no mistake, converting with a close-range volley.
After the break, Tottenham started the brighter and Jos Hooiveld knocked Danny Rose's cross past his own 'keeper.
Southampton responded though and Rickie Lambert sidefooted home after a superb reverse ball from Lallana.
Adebayor had the final word, however, smashing home a left-footed strike on 64 minutes after the ball fell to him in the box.