The African side – who along with Panama had already been eliminated before their clash at the Mordovia Arena – last tasted victory at the 1978 tournament when they beat Mexico 3-1.
Before their second-half fightback, Panama had looked like sealing a maiden World Cup victory when Jose Luis Rodriguez's long-range strike was deflected in by Yassine Meriah for an unfortunate own goal after 33 minutes.
Tunisia had been woeful in the opening period, but started the second half strongly and pulled level six minutes after the restart when Fakhreddine Ben Youssef tapped in from close range after a flowing move.
Sunderland forward Wahbi Khazri – who scored in the 5-2 defeat to Belgium last time out – was Tunisia's brightest spark throughout and he got the goal he deserved after 66 minutes, slotting home after another impressive team move.
Panama huffed and puffed in the closing stages, but were unable to find a goal that would have ended their memorable World Cup campaign with a flourish.
With little at stake, it was hardly surprising that the game started at a tepid pace.
Naim Sliti enjoyed an early sight of goal, but cracked a half-volley well off target from outside the area, while Rami Bedoui's header was comfortably dealt with by Jaime Penedo.
Panama looked significantly more organised than in their capitulation to England and were rewarded with the opening goal shortly after the half-hour.
Rodriguez picked up the ball from Roman Torres 25 yards out and his well-struck shot took an almighty deflection off Meriah to wrong-foot goalkeeper Aymen Mathlouthi and nestle in the back of the net.
That goal appeared to spark the African side into life and they soon wasted two clear opportunities to pull level.
Ben Youssef flashed a header wide of Penedo's far post from a teasing cross before Khazri thumped a volley over from a promising position at the back post.
Khazri again came close before the interval when his initial shot was blocked and Penedo scrambled away his follow-up effort.
Tunisia looked a team rejuvenated at the start of the second period and pulled level after 51 minutes from an incisive move that carved open the Panama backline.
After dancing past two defenders on the edge of the area, Sliti found Khazri down the right and the latter's low cross was converted by the unmarked Ben Youssef just six yards out.
The Al-Ettifaq forward should have scored a second minutes later, but his low effort was kept out by the foot of Penedo.