Newcastle's first-half capitulation was similar to its opening-weekend 4-0 loss at Manchester City but at least the team had the excuse of playing with 10 men for most of that match.
Here, they were blown away from the first whistle by a lively and dynamic Everton team which appears to be growing in belief under Martinez, who replaced David Moyes during the offseason.
Martinez' loan signing of Lukaku on transfer deadline day already seems to be a masterstroke, and a major oversight by Chelsea given the striker netted 17 times on loan at West Bromwich Albion last season. He has scored three times in two league games for Everton, while the three strikers in Chelsea's squad Samuel Eto'o, Fernando Torres and Demba Ba have yet to hit the target this season.
"At times he was unplayable,'' Martinez said of Lukaku. "Today he looked a player enjoying his football and at home here.''
After scoring on his debut nine days ago at West Ham, he took just five minutes to score against Newcastle by powerfully sidefooting a shot through goalkeeper Tim Krul's grasp after being set up by Belgian teammate Kevin Mirallas.
Lukaku turned provider in the 25th minute by slipping a pass through the middle to Barkley, who took a first touch before quickly shooting into the corner past Krul. It capped another impressive performance by the locally born 19-year-old midfielder, who has already been called up by England this season.
If Newcastle's defending was poor for the first two goals, it was nothing compared with the third.
Everton goalkeeper Tim Howard's long punt downfield bisected Newcastle's central defenders, allowing Lukaku to round Krul, cut inside Fabricio Coloccini and smash the ball into an empty net from five yards out.
Clearly unhappy at his team's performance, Newcastle manager Alan Pardew made a double substitution at halftime and one of the replacements, Cabaye, made an immediate impact by blasting a swerving shot into the top corner in the 51st.
From thinking about damage limitation, the visitors suddenly had hope and were much better after the break. And when Remy outmuscled Phil Jagielka to prod home a close-range finish, Newcastle suddenly had designs on a draw.
However, Remy's shot over the bar in the third minute of stoppage time was the closest it came to an equalizer. Newcastle has seven points from its opening six matches.
Everton midfielder Gareth Barry made his 500th Premier League appearance, becoming only the 10th player to reach that milestone.
-AP
