It kept the Merseysiders sixth in the table, maintaining an unbeaten home record in the Premier League under manager Ronald Koeman, who replaced Roberto Martinez in the close season.
West Ham have now lost four of their five away games and could drop into the Premier League's bottom four after Stoke City's game with Swansea City on Monday.
As is often the case, French international Dimitri Payet carried West Ham's greatest threat.
He helped set up Pedro Obiang for the away side's one real first half chance but the midfielder scooped his shot over the bar.
With only one shot each on target during that opening 45 minutes there was little to match the drama of the corresponding fixture last season when West Ham trailed 2-0 in the 77th minute but won 3-2, Payet scoring the winner in added time.
Goalkeeper Adrian produced one fine save before the interval to deny Barkley, but five minutes after the resumption he could only parry Seamus Coleman's drive and Yannick Bolasie reacted quickest, giving Lukaku the easiest of finishes for his seventh goal of the season.
It continued his run of regular goals against the Londoners and although Adrian denied him another, the Belgian international supplied an assist for Barkley to double the lead in the 75th minute.
Barkley began the move inside his own half and raced forward to half-volley in Lukaku's astute pass.
Although Everton's goalkeeper Joel Robles had to make saves from Michail Antonio and Mark Noble, the home fans were convinced they should have had a penalty just before the finish when Angelo Ogbonna appeared to foul Idrissa Gueye.
"It was a total team performance," Koeman told Sky Sports.
"Ross Barkley had more impact in the last part of our attacking, not only in scoring but he was dangerous throughout.
"He can be very good, but it is all about knowing what you need to do. Sometimes I have to shout too much, he needs to run more."
West Ham's manager Slaven Bilic, a former Everton player, said: "We should have done better. The first goal was very cheap, we gave it away, and after that they were always dangerous on the counter-attack. So a big disappointment."
(Reporting by Steve Tongue; Editing by Toby Davis and Ian Chadband)
