Barkley's shot, deflected off Burnley defender Ben Mee, put Everton 2-1 up in the 71st minute and the league's top scorer Romelu Lukaku made sure of the win three minutes later with his 24th strike of the season.
England international Barkley had been the victim of an assault in a bar on Sunday and was then at the centre of a controversial column in The Sun newspaper. He was given a standing ovation when he was substituted in the final moments.
Barkley, who also cleared off the line twice, was booked for over-celebrating with fans when he put the team ahead.
"Of course, I can understand. Because I think what happened last week had a really big impact on him. I think he was focussed on the football side this week and also this afternoon," Everton manager Ronald Koeman told reporters, adding that he did not consider leaving Barkley out of the team.
"I think it is the best way to play football and forget what happened last week," the Dutchman said.
A 52nd-minute Sam Vokes penalty had brought Burnley level after Phil Jagielka had scrambled Everton ahead three minutes earlier.
Barkley offered reminders of his quality throughout as Koeman's team ensured Burnley remain without an away win this season.
Burnley started confidently, however, and went close to an opener in the 19th minute when Barkley was forced to clear a powerful Michael Keane header off the line.
AWFUL PASS
The visitors should have taken the lead in the 34th minute when an awful back-pass from Jagielka played in Burnley striker Sam Vokes but, clear on goal, the Welsh international shot tamely straight at Joel Robles.
Everton ended the half strongly, however, Mason Holgate bringing a fine save out of Burnley keeper Tom Heaton with a low drive towards the bottom corner.
Koeman brought on an extra striker at the interval with Enner Valencia replacing Idrissa Gana and the Ecuadorean forward immediately tested Heaton with a fierce drive.
The home side went ahead when Ashley Williams flicked a corner from Kevin Mirallas goalwards and Jagielka scrambled the ball over the line.
The Everton lead lasted barely three minutes, though, Robles inexplicably sliding through the back of Vokes as he moved harmlessly away from goal and the Burnley forward converted the spot-kick.
Mirallas wasted a good opportunity when found by Barkley inside the area but he shot meekly at Heaton but the Beglian did better when his well-struck effort flew against the post.
The pressure paid off when Barkley wriggled space for himself and his shot deflected off two Burnley defenders and crept into the bottom corner.
There was nothing lucky about Everton’s third, Lukaku spinning superbly to turn past Keane and blast a shot past Heaton at the near post.
Lukaku has now scored in nine successive home games – the last player to achieve that feat was Dixie Dean in 1934.
Everton moved up to fifth in the table, above Arsenal and Manchester United who both have three games in hand on the Merseyside club.
(Editing by Ed Osmond)
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