The Toffees saluted 5-3 in an entertaining second round fixture at Oakwell which saw the home side skip away to a two-goal lead.
Sam Winnall and Marley Watkins had the League One Tykes to goals to the good inside 28 minutes before Kevin Mirallas and Steven Naismith got the Premier League visitors back on level terms with 51st and 59th minute efforts.
An own-goal from Marc Roberts early in the first half of added time had Everton breathing easy before Lukaku wrapped it up in the 115th minute, sending Roberto Martinez's men through to the third round where they will meet Reading at the Madejski Stadium in September.
2015/16 CAPITAL ONE CUP - Second round
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!