It says focusing on these diseases would narrow the survival gap between the richest and poorest children adding that Pneumonia and diarrhoea account for one-third of all global deaths among children under 5yrs.
Unicef's report, in advance of a child-survival initiative, calls for better access to vaccines and antibiotics.
The Unicef Executive director Anthony Lake, said it was a question of commitment and funding. "We know what works against pneumonia and diarrhoea - the two illnesses that hit the poorest hardest," he said.
"Scaling up simple interventions could overcome two of the biggest obstacles to increasing child survival and help give every child a fair chance to grow and thrive."
Nearly 90 per cent of deaths from pneumonia and diarrhoea occur in sub-Saharan Africa and South Asia.
The report says that more than two million children's lives could be saved in the 75 countries with the highest death rate if the poorest children received the same care and treatment as the wealthiest 20% in those countries.
New vaccines against the major causes of pneumonia and diarrhoea are already available.
While most low-income countries have introduced the Haemophilus influenza type b (Hib) vaccine and pneumococcal conjugate vaccines, they urgently need to introduce them into routine immunization programmes, the report said.
The prevention and treatments for both diseases include increasing vaccine coverage, encouraging breastfeeding, hand-washing with soap and expanding access to safe drinking water and sanitation.