Belarus' disciplined defense held Spain to one shot on target in the first half, but Spain's insistence led to Xavi scoring the 61st-minute opener before substitute Negredo added a second goal in the 78th.
Substitute Sergei Kornilenko snatched a consolation goal for last-place Belarus on the break in the 89th.
The victory gave Spain 17 points in Europe Group I. France has 14 before both play on Tuesday.
