Tunis led early in Algeria through Ahmed Akaichi but a brace from Akram Djahnit saw Setif take control at home.
Akaichi then registered a double of his own with 18 minutes remaining at the Stade du 8 Mai 1945 to equalise but Tunis were unable to find a winner, ensuring the Tunisian powerhouse failed to reach the final four of the African continental competition for the first time since 2009.
The draw saw second-placed Setif move to nine points in Group B of the Champions League, one point adrift of leaders CS Sfaxien.
Tunis moved off the bottom of the standings above Al Ahli Benghazi on goal difference but have just four points from five matches and will be unable to overhaul Setif with just one game remaining.
The reigning Tunisian champions arrived in Algeria knowing anything less than two wins from their remaining pair of Champions League fixtures would ruin their chances of playing in the semi-finals for the fifth straight year.
And the game started well for Sebastien Desabre's men with Akaichi volleying Haythem Jouini's flick-on from a long throw past Setif goalkeeper Abderaouf Belhani in the seventh minute.
But the home side hit back just before the half-hour mark with Djahnit scoring from the spot after Sofiane Younes had been tripped in the box.
Djahnit then put Setif ahead four minutes after the break, playing a neat one-two with Abdelmalek Ziaya to completely open up Tunis' defence, before the 23-year-old striker rounded the keeper to score.
Akaichi would level the match in the 72nd minute, tapping Khaled Gharsellaoui's cross into the net after Fousseny Coulibaly's 30-yard drive came back off the post, but it mattered little as Setif held on to win and advance into the semi-finals.
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