Veteran midfielder Leon Osman capped off Everton's evening with a third goal late on following a swift counter-attack.
Here, Sports Mole takes a closer look at the 90 minutes to establish whether the result was fair.
On target: 3
On target: 6
Was the result fair?
Everton deserved three points without question, yet one could argue that 3-0 flattered them slightly. Newcastle created more chances but were wasteful, while the Blues rode their luck on occasion and managed to take some of the opportunities they carved out.
The Magpies matched Everton for spells of the match, but were vulnerable on the break and squandered the goalscoring opportunities they created. Papiss Cisse's positioning was good, while his finishing was anything but. Luuk de Jong looked out of his depth, and Yoan Gouffran and Vurnon Anita both missed sitters, so it's difficult to argue that they deserved anything tonight.
Roberto Martinez will be pleased with his side's performance this evening. They may have created fewer chances than their opponents, but they were absolutely devastating on the counter-attack and clinical when it counted. Barkley and Osman ruled the midfield, and Gerard Deulofeu's flare was an absolute spectacle. Young defender John Stones should also be singled out for plaudits.
Sports Mole's man of the match
Gerard Deulofeu: The young Spaniard was a cut above the rest this evening, displaying the kind of skills that will eventually see him graduate to the Barcelona first team. He was involved in virtually everything the Blues created and struck fear into the heart of the Newcastle defenders every time he touched the ball.
Sitters from both Gouffran and Anita are contenders for this prize, but it is the latter who was guilty of the most glaring miss, lashing the ball wide from mere yards out after Hatem Ben Arfa had set him up for what was practically an open goal.
Referee Lee Mason didn't have much to do this evening, handing out only one yellow card. Gareth Barry was on the receiving end, and it was as clear a booking as you're ever likely to see. Mason should perhaps have punished Barkley for a blatant dive in the first period, but this oversight did not have a bearing on the outcome.
Newcastle: The Magpies will be hoping to bounce back from this evening's trouncing when they pay a visit to Southampton next weekend.
Everton: Everton's quest for European football continues next weekend when they travel to relegation-threatened Fulham.