Water don't have to be the side product of reaction between a base and an acid because at times, the relative acidity or basicity are being compared.
For example, in the nitration of benzene,
HNO3 acts as a base due to presence of stronger acid H2SO4.
Would you consider HNO3 as a base or an acid? Do you think the reaction gives you water despite HNO3 acts as a base?
The underlying principal in neutralization, is that H+ + OH- --> H2O
So, do you think you have a source of H+ from the reaction you gave?