Midfielder Rakitic struck a fierce 25-metre drive that took a slight deflection off Belarus defender Dimitry Verkhovtsov to wrongfoot goalkeeper Yury Zhevnov.
Croatia have played a game more than their rivals with 17 points from eight matches, four behind group leaders England and three ahead of third-placed Ukraine who beat Andorra 5-0.
Croatia face England at Wembley on Wednesday and must avoid defeat to have any chance of topping the group.
They deserved their lead on Saturday having created several early chances, with Dario Srna firing past the post in the 15th minute after an indirect free kick just inside the area.
Belarus upped the pace after the break as the hosts mostly defended their lead - a task that became harder after defender Vedran Corluka was sent off in the 79th for two bookings. But Croatia held on with 10 men to secure an important victory.
"We are very happy to have won these three points. It was difficult to play against such a defensive side and three great saves by (Vedran) Runje late in the match helped us keep the lead," said midfielder Ognjen Vukojevic.
The group winners qualify for the finals in South Africa, with the eight best runners-up going into the playoffs.
