England international Barkley netted with a magnificent solo goal that gave Everton the lead after 22 minutes and showcased just why is viewed as one of the Premier League's most exciting prospects.
Barkley's effort will grab the headlines, but the result owed more to a superb team performance from Roberto Martinez's men, and they deservedly increased their advantage early in the second half thanks to a simple close-range strike from Romelu Lukaku.
And the gloss on a superb Everton display was applied in the closing stages, as Leon Osman rattled home a third to further illustrate their all-too-apparent superiority.
The victory marks the first time that Everton have completed a league double over Newcastle since 1999, but more importantly moves them within six points of fourth-placed Arsenal - who they host on April 6 - with a game in hand after the Londoners drew 2-2 with Swansea City.
Newcastle striker Papiss Cisse almost picked up where he left off after his last-gasp winner against Crystal Palace on Saturday when he came close to breaking the deadlock early on.
The Senegal international connected with a near-post corner from Paul Dummett, but his shot was saved by Tim Howard before Yoan Gouffran's follow-up effort was blocked on the line.
But Everton quickly began to dictate matters and penned the hosts inside their own half for much of the opening stages.
The visitors' dominance looked set to pay dividends in the 16th minute as Osman played Lukaku through on goal, only for Newcastle goalkeeper Tim Krul to produce an outstanding save.
However, Everton's opener did soon arrive as Barkley lit up St James' Park with a contender for goal of the season.
The 20-year-old picked up the ball from well inside his own half after a Newcastle corner, sprinting all the way to the edge of the area before cutting inside past a string of recovering Newcastle defenders and unleashing a thunderous left-footed strike into the top corner.
Newcastle looked to respond and demonstrated plenty of industry, but their lack of creativity in the final third was their undoing as they struggled to test Howard.
The hosts' failure to break down the Everton defence was in stark contrast to the pace and guile of Martinez's men, who moved into a commanding position shortly after the interval.
On loan Barcelona winger Gerard Deulofeu fired a warning shot by flying down the right and drawing a strong save from Krul.
Yet Newcastle did not learn from that close call, and found themselves two behind in the 52nd minute as Deulofeu latched onto a clever ball from Osman and delivered a precise low right-wing cross for Lukaku to tap home.
And the hosts' disappointing evening was summed up 12 minutes from time, Vurnon Anita shooting wide with the goal gaping before Osman finished off another sweeping Everton attack to emphatically end their run of five away Premier League fixtures without a win.
