The South African side looked to carry on their fairytale run on the continent and run out a strong line-up to withstand the two-time African champions.
Dan Malesela's side were put to the test as early as the seventh minute when Victor Mbaoma headed home a cross from Abdulrahman Bashir.
As Galaxy recuperated, the hosts fluffed a big chance to a second when Jean Marie Guera missed a rebound from Stanley Dimgba with the visitors in a spot of bother six minutes later.
Possession based football from Galaxy had the Nigerians chasing shadows, as Tshegofatso Nyama squandered a clear chance with their opposite number in no man's land. Momentum remained with Galaxy, who had Tshepo Chaine's effort from Mosha Gaolaolwe's cross ruled out for offside by the assistant referee on the brink of halftime.
Enyimba increased their lead moments in the second half Martin Ursule got on the end of a good move for an exquisite finish past Ludwe Mpakumpaku.
Chaine instantly threatened a reply five minutes later, but missed a point blank header following a ball into the danger area.
Ursule threatened their third and his second of the day in the final 20 minutes, but Mpakumpaku made a smart block whilst Sizwe Mdlinzo fired blanks from close range at the other end.
The Rockets tried a refreshed approach close to the end, but the Nigerians maintained balance for a first-leg victory with the return leg set for Mbombela next weekend.