Max-Alain Gradel missed the first spot-kick during the opening half after grabbing the ball from Arsenal forward Nicolas Pepe, who won the penalty and wanted to take it.
Out-of-favour AC Milan midfielder Franck Kessie was entrusted with the second spot-kick, awarded for handball midway through the second half.
Niger goalkeeper Kassaly Daouda, who had brilliantly foiled Gradel, could not do it again, going the wrong way as Kessie planted the ball in the left corner.
It was an unconvincing performance by the 1992 and 2015 African champions, given they are ranked 56th in the world, 51 places above Niger.
Niger were playing for the first time under Frenchman Jean-Guy Wallemme who was only appointed last week.
The 52-year-old former defender previously coached Congo Brazzaville, three Algerian clubs and one in Morocco.
Ivory Coast share first place in Group K with Madagascar, who beat Ethiopia 1-0 in Antananarivo thanks to a first half goal from Rayan Raveloson.
The Malagasy team were the surprise package of the 2019 Cup of Nations in Egypt, stunning Nigeria and surprising the Democratic Republic of Congo before losing to Tunisia in the quarter-finals.
Coach Nicolas Dupuis, who combines coaching Madagascar with managing a French lower league club, was rewarded with a new four-year contract.
He was satisfied with the tentative performance against Ethiopia given the poor state of the national stadium pitch and limited preparations.
“We need a new venue because the pitch we used today was unplayable,” said the 51-year-old who rose from obscurity to worldwide recognition during the 2019 tournament.
“Now we face a difficult trip before playing Niger Tuesday. We must manage fatigue and will have insufficent time to prepare before the match in Niamey.”
Limited flights, seats and direct routes mean Madagascar, like many African national teams, face logistical headaches having to play two matches in a seven-day international window.
Some of the Malagasy squad left the vast Indian Ocean island at 0300 local time (midnight GMT) Sunday while the rest followed 12 hours later.
“What pleased me about the victory over Ethiopia was our ability to defend a narrow advantage. That was a hallmark of our performances in the previous qualifying competition,” added Dupuis.