The visitors got off to a dream start, scoring after just six minutes of play as Ighodaro Osaguona, allowed a free header by Tefu Mashamaite, headed home a free-kick from the right channel at the far post.
It was uphill all the way for Chiefs from there as the Moroccan side set up their stall to contain Stuart Baxter's side.
But far from parking the bus, Raja marked tightly in midfield and gave Chiefs no breathing space in midfield, often winning the ball back quickly and looking to hit on the counter.
Chiefs were too predictable in the first half as the Moroccans comfortably stopped their attacks, and Raja would have been 2-0 up at half-time were it not for Brilliant Khuzwayo, who came off his line smartly to deny Ighodaro one-on-one.
It ended 0-1 at half-time.
Three minutes after the restart it should have been 2-0 to Raja after Molomowandau Mathoho misjudged a routine header, allowing Ighodaro through on goal, and after Khuzwayo saved his initial effort, the Nigerian striker put the rebound into the side-netting with the goalkeeper on the floor.
Chiefs fashioned their first decent attempt at goal in the 53rd minute as Siboniso Gaxa crossed for Katlego Mphela, whose first-time shot from just inside the box flew narrowly over the crossbar.
A minute later Siphiwe Tshabalala's cross found Parker in space in the box, but a brilliant block from a Raja defender denied Chiefs.
Ten minutes later Parker crossed for Mphela on the penalty spot, but his glancing header went inches wide of the far post as Chiefs started to turn the screw in search of an equaliser.
The best chance of the match fell to substitute Siphelele Mthembu in the 86th minute, but after being played in one-on-one, with Siphiwe Tshabalala also at his side he could have passed to, the striker missed the target using the outside of his boot.
Chiefs go to Morocco for the second leg on April 4 and have it all to do.
Chiefs XI: Khuzwayo, Gaxa, Mashamaite, Mathoho, Masilela, Katsande, Letsholonyane, Masango (Lebese 76'), Tshabalala, Mphela (Mthembu 82'), Parker (Ekstein 75')
Raja XI: Askri, Oulhat, Ibira, Karrouchy, Belam Kadem, Behammer, Guehi, Vivien, Issine, Ighodaro, Salhi