A piledriver from Mejdi Traoui with seven minutes remaining gave Tunisia a point they barely deserved.
Tunisia took an early lead with one of their few first-half chances as Issam Jooma scored from an acute angle.
But Moustapha Sall punished an error by Rahdi Jaidi to equalise on the stroke of half-time and Diomansy Kamara's close-range effort put Senegal ahead.
Then, with Tunisia apparently going nowhere, Traoui cracked the ball into the top-left corner from 25 yards out.
Senegal played by far the more positive football, though they did not do enough to rank themselves as leading contenders to win the tournament.
The Teranga Lions made a lively start, pinning Tunisia in their own half in the opening minutes, with Mamadou Niang shooting wide after a good run.
But Tunisia went ahead in the ninth minute thanks to Jomaa's precision strike.
The France-based striker, who plays for Caen, made a run down the left flank, played a one-two with Wissem Bekri, and smashed the ball in from a tight angle.
The heat appeared to take its toll as the game failed to pick up pace, and the Tunisia defence laid a tight offside trap.
Senegal were restricted to long-range efforts, and another Niang shot went wide on 23 minutes after the Marseille striker ran at the Tunisia defence.
But the organised play of the Carthage Eagles' back four came to naught with a defensive error in first-half stoppage time.
Jaidi failed to clear his lines, miscueing into the path of Sall, who raced goalwards and fired in from 15 yards.
Immediately after the break Senegal captain El-Hadji Diouf burst into the penalty area but missed the target.
Soon after Diouf laid on a lovely pass to Kamara, but his effort was also wide.
On the hour mark the Teranga Lions passed up another opportunity, as Niang misfired from close range.
But their attacking play got the reward it deserved with Kamara stabbing the ball home from six yards in a goalmouth melee.
Tunisia appeared to be heading for defeat, until Traoui's moment of brilliance in the 83rd minute.
But there was no doubt that Senegal had been the better team overall.
Tunisia: Kasraoui, Haggui, El Bekri, Jaidi, Felhi, Mnari, Zouaghi (Ben Dhifallah 80), Traoui, Santos (Zaiem 63), Jemaa (Mikari 86), Chikhaoui.
Subs Not Used: Mathlouthi, Nefzi, Ghezal, Abdi, Ben Saada, Nafti, Ben Fredj, Meriah, Chermiti.
Booked: Santos, Traoui, Zaiem.
Goals: Jemaa 9, Traoui 82.
Senegal: Sylva, Diawara, Abdoulaye Faye, Beye, Guirane, N'Doye (Diop 63), Sall, Mendy (Camara 61), Kamara, Niang (Gueye 88), Diouf.
Subs Not Used: Ndiaye, Coundoul, Sonko, Sarr, Ibrahima Faye, Diatta, Papa Waigo, Sougou, Ba.
Booked: Mendy, Kamara.
Goals: Sall 45, Kamara 66.
Ref: Yuichi Nichimura (Japan).
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