Mohamed Manser struck first just after the hour mark but his side were punished for failing to build on their lead in their Africa Cup of Nations opener
With Zambia and DR Congo drawing 1-1 earlier in the day, Tunisia looked set to assume top spot in Group B despite being on the back foot for sustained spells in the second half.
Rui Aguas’ side, who are only appearing in the African showpiece for the second time, struck the post inside the first two minutes in an encouraging first-half display.
However, they were undone by a move of real quality as Stephane Nater found Ahmed Akiachi who squared for Manser to finish from inside the six-yard box.
Cape Verde hit back, though, and salvaged a point when Heldon calmly converted from the spot to deny a side ranked 18 places above them in the Fifa Ranking.
It leaves things as you were in the group, with Tunisia and Cape Verde facing Zambia and DR Congo respectively next.
Cape Verde may be somewhat unfancied for the tournament but their entirely overseas-based XI made a bright start, with Steaua Bucharest defender Fernando Varela hitting the post from a free kick after just a minute.
Following a sluggish 10 minutes, Tunisia grew into the game and Ahmed Akaichi saw his header palmed away by Vozinha.
Kuca threatened next for Cape Verde – his strike kept out by Hamza Mathlouthi at his near post – before Djaniny shot straight at the Tunisia goalkeeper after being played in on goal by Heldon.
It was then Djaniny who was set to become provider but the Santos Laguna man put too much on his cross as it evaded the unmarked Kuca in the centre.
Tempers flared when Ali Maaloul brought down Heldon the edge of the area with the sides disagreeing on whether the foul took place in or outside of the box.
Babanco’s resulting set-piece found Kuca via the wall but the Estoril forward failed to find a finish from close range as Cape Verde were unable to gain the reward their first half showing perhaps warranted.
Georges Leekens’ men started the second half with much more impetus, but Cape Verde again looked dangerous on the counter – with Kuca’s shot cleared off the line by Ben Youssef after some slick build-up play involving Babanco and Heldon.
Tunisia’s almost took the lead just after the hour when Manser headed against the crossbar and, although Yassine Chikhaoui bundled in the rebound, referee Eric Otogo-Castane adjudged there to have been a foul on the goalkeeper.
Eventually, the quality of Leekens’ side showed as Nater found Akiachi with a well-angled throughball and the ES Tunis forward squared across goal for Manser to crash home the opener.
Aguas’ men were level 12 minutes from time when Heldon tucked away a penalty, having been felled by Youssef inside the area, as Cape Verde got their campaign up and running with a positive result.