Base current and Vce relation in NPN transistor output characteristics
The depletion region inside base widens with increasing collector voltage. Because of this, the neutral base width reduces. This leads to reduced base recombination current (\$I_{Br}\$). Now Let us think what happens to collector current and base current.


Since the electrons (majority carriers) injected from emitter experience less recombination in the base, the collector current increases. 
Since recombination current is reducing, the back injection of holes (minority carriers) from base to emitter will increase to maintain the base current fixed. This slightly increases the base-emitter voltage. 


I think you have slightly mixed up the above two points.