Moore scored 10 minutes before the half time against his old club with a header after meeting a precise cross from Jonathan de Guzman.
Pablo Hernandez set Michu up first on eight minutes, but the forward sent his left-footed strike over the bar from close range.
Swansea looked threatening on the counter and came close to taking the lead when Luke Moore played Michu through, but once again the Spanish striker sent his effort past the far post.
Moore's goal prompted a positive response from the home side and Lukaku equalised on 40 minutes after sending a measured drive home from close range.
De Guzman sent a strike from distance just over the crossbar soon after as an entertaining first 45 minutes ended 1-1.