Also among the top 10 nations that have made the greatest strides in tackling such deaths are Liberia, Rwanda, Indonesia, Madagascar, India, China, Egypt, Tanzania and Mozambique, Save the Children found.
On the more problematic end of the spectrum, those making the least progress were Haiti, Papua New Guinea and Equatorial Guinea, said the non-governmental group's report.
The rate of unnecessary deaths of children under five still remains high in Niger. But it has been reduced by a dramatic two thirds: plunging from 326 in 1,000 back in 1990 to 114 out of 1,000 in 2012.
A large part of Niger's success has been its progress across income groups. One of the world's poorest nations, Niger nonetheless implemented nutritional programs and access to free care for pregnant women and children.
The report analyzed how 75 countries, which account for nearly all maternal and child deaths, are progressing towards the United Nation's Millennium Development Goal on child mortality.
"Despite having scarce resources and recurring droughts, Niger has cut the number of under-fives dying unnecessarily by nearly two thirds since 1990 and is on track to achieve the UN's global goal on child mortality," the report said.
"The country's progress is striking because -- unlike others -- it has managed to do better across all income groups, and in the countryside as well as urban areas."
But income inequality in sub-Saharan Africa -- where most child deaths occur -- actually worsened from 1998-2008, the study found.
"We are making historic gains in the fight against child deaths but this headline success also often masks that poor children are being left behind and, in extreme cases, are doing worse," said Save the Children's global campaign director, Patrick Watt.
Four million children could have been saved in this timeframe if the fight against child mortality were spread out in an economically balanced way, the NGO said.
Save the Children has urged governments to implement "national healthcare plans that reach every child, including newborns, with the objective of reaching full coverage by 2030" and "reduce malnutrition so that every child has the nutrition they need to survive and thrive."