Gareth Barry scored on his landmark 600th Premier League appearance to help Everton come from behind to beat Middlesbrough at Goodison Park.
The home side responded, when Barry, lurking at the back post from a corner, fired in for his 52nd Premier League goal.
Lukaku scored his fourth league goal of the season when he got a faint touch on Yannick Bolasie's cross to give Everton a two-goal cushion at half-time.
Middlesbrough worked hard after the break but could not break down the well-organised hosts, who rise to second after four wins and a draw, their best start to a Premier League season.
Man of the match Gareth Barry