Always. Lower numbers do not necessarily go with what comes first alphabetically. If there is a tie between two groups and the same number, then the alphabetically-ordered group gets the lower number.
—OH always gets the lowest number.
In general the priorities are thus:
C=O > OH > NH2 > alkene ~ alkyne
Carbonyls receive priority over alcohols; alcohols receive priority over amines; and amines receive priority over alkenes, which receive about the same priority as alkynes.