Having dominated but lost the first leg at FNB Stadium 1-0 a fortnight ago, it was much of the same in North Africa as Amakhosi wasted chance after chance, only for Raja to score twice late on through Osaguona.
Stuart Baxter had made four changes to the side from that first leg, with Itumeleng Khune, Morgan Gould, George Lebese and Matthew Rusike coming into the side.
With a feverous home support spurring them on, it was Raja who got out of the blocks quickest as Chiefs struggled to string together passes and maintain possession.
The lack of focus almost cost them in the 15th minute when a free-kick was taken short to Sahli, who ran at Khune. But rather than having a shot, he decided to square and the moment was lost.
Chiefs got their first chance in the 19th minute when Tsepo Masilela was brought down on the edge of the area, but Bernard Parker’s free-kick hit the wall.
Amakhosi came closest to scoring in the 25th minute when some quick movement in the box saw Lebese shoot at goal, but his goalbound effort was deflected for a corner.
Tefu Mashamaite needed to be at his best 10 minutes later when Mabide got the ball in the area with his back to goal, turned and fired off a shot, but the defender recovered to make a great block.
Chiefs suffered an injury setback just before the break when Morgan Gould was taken off, to be replaced by Mulomuwandau Mathoho.
Whatever Baxter’s halftime talk was, it seemed to have done the trick as the visitors completely dominated the second half.
They should have been level just three minutes after the restart when Lebese was played clean through on goal, but he shot wide from 15 yards out.
Masango then missed three good chances to give Chiefs the lead. First his diving header from Rusike’s cross went straight at the keeper, before the midfielder fired a thunderous volley inches over the crossbar.
Masango really should have done better on 78 minutes when Rusike again played him in but, rather than hit it first time, he took a touch in the small box and was closed down.
And then, on 89 minutes, the sucker-punch.
Having played so well for most of the match, they switched off with a minute to go when Siboniso Gaxa inexplicably chested a cross into the path of Osaguona, who slotted past Khune from close range.
And, as if to add insult to injury, Osaguona got another four minutes into stoppage-time, burying after a deflected cross into the area fell at his feet.
So Chiefs crash out 3-0 on aggregate, meaning South Africa will have no representitives in the Champions League second round after Mamelodi Sundowns were also eliminated earlier in the day.
Chiefs starting XI: Khune, Gaxa, Mashamaite, Gould (Mathoho 44), Masilela (Moleko 46), Letsholonyane, Katsande, Lebese, Masango (Mthembu 89), Parker, Rusike
Raja XI: El Allouch, Karouchi, Oulhaj, Belmkadem, Jbira, Bamaamer, Kouko, Salhi, Mabide, Issine, Osaguona