Following a slow start, Esperance drew first blood when Adelraouf Benguit met a delivery from Iheb Mbarki to turn home inside the 32nd minute.
Esperance looked to increase their advantage soon afterwards, but were undone by poor finishing inside the area and strong defending from the visitors.
Raja came out renewed for the second half and instantly had the home side on the back foot in the earlier exchange.
This spell of play coincided with the leveller which came in the 49th minute courtesy of a fine finish from Fabrice Ngah after poor goalkeeper from Moez Ben Cherifa.
That was the first time the Tunisian giants and defending champions have conceded a goal in this year's group stage event, with Raja given a tail up their sleeve.
Raja went ahead after the 67th minute when Badr Banoun found space in the area to fire home after the hosts went to sleep at the back.
The Tunisians switched to the bench in the last nine minutes and introduced Fadi Ben Choug, who replaced Khenissi up front. Choug wasted no time announcing his arrival as he drew the home side level seconds after entering following a delivery from Mohamed Yaakoubi.
Honours even was how the match finished amidst a few late openings, with the group's top-two safely into the quarter-finals.