The match in Suez saw few clear chances created by either side, with Tunisia captain Msakni seemingly having stepped up to seal all three points for his team.
Naim Sliti was brought down in the box late in the first half and Msakni made no mistake with the resulting spot-kick, but Angola hit back and claimed a deserved point when Djalma slotted home.
Angola had the better of the opening 45 minutes but Tunisia took the lead in the 34th minute.
A sweeping counter-attack led to Sliti cutting inside Paizo and shaping to shoot, with the defender's desperate lunge bringing him down, leaving Msakni to convert from 12 yards.
Gelson Dala fired off target as Angola continued to press, but Srdjan Vasiljevic's team appeared unable to find a way to break Tunisia down.
Msakni had a penalty appeal rejected in the 71st minute when referee Bamlak Tessema Weyesa adjudged the striker to have gone down too easily in the area.
But Tunisia has kept just one clean sheet in its last 17 Africa Cup of Nations matches and Angola levelled with its next attack.
Goalkeeper Farouk Ben Mustapha made an error in pushing Mateus' shot back into the danger zone, leaving Djalma to pounce from close range.
Tunisia had late chances to retake the lead but, after finding space in the box with some neat footwork, Wahbi Khazri curled his low shot wide, then Msakni drilled straight at Tony Cabaca in added time.