I'm writing as I wondered the same thing and found this thread.
Here it goes: Suppose you wish to estimate
y=x1*b1+x2*b2+u
You are interest in the estimate of b1. Luckily, x1 is completely exogenous, but x2 is endogenous. Then OLS will yield a biased estimate of both b1 and b2. If you run IV with an instrument for x2, the b1 will still be biased. If, however, you do 2SLS running x2 on the instrument AND x1 in the first stage, and then do OLS on
y=x1*b1+xx2*b2+u
where xx2 is the fitted values from the first step. THEN your estimates of both b1 and b2 are consistent.
I recently read a working paper which shows that the estimator of beta1 will not be biased if x1 and x2 are uncorrelated or if x2 precedes x1, for example by x1 = gamma*x2 + eta.