We present a study of the host galaxies of active galactic nucleus (AGN) selected from the zCOSMOS survey to establish if accretion onto supermassive black holes (SMBHs) and star formation are explicitly linked up to z ~ 1. We identify 152 galaxies that harbor AGN, based on their X-ray emission (L 0.5-10 keV>1042 erg s-1) detected by XMM-Newton observations of 7543 galaxies (i acs < 22.5). Star formation rates (SFRs), including those weighted by stellar mass, of a subsample are determined using the O IIl3727 emission-line luminosity, corrected for an AGN contribution based on the observed O IIIl5007 strength or that inferred by their hard (2-10 keV) X-ray luminosity. We find that an overwhelming majority of AGN host galaxies have significant levels of star formation with a distribution spanning ~1-100 M yr-1; their average SFR is higher than that of galaxies with equivalent stellar mass (M *>4 X 1010 M ). The close association between AGN activity and star formation is further substantiated by an increase in the fraction of galaxies hosting AGN with the youthfulness of their stars as indicated by the rest-frame color (U-V) and spectral index Dn (4000); we demonstrate that a mass-selected sample is required to alleviate an artificial peak in the AGN fraction falling in the transition region due to the fact that many 'blue cloud' galaxies have low mass-to-light ratios in luminosity-limited samples. We also find that the SFRs of AGN hosts evolve with cosmic time in a manner that closely mirrors the overall galaxy population and naturally explains the low SFRs in AGNs (z < 0.3) from the SDSS. We conclude that the conditions most conducive for AGN activity are a massive host galaxy and a large reservoir of gas. Furthermore, a direct correlation between mass-accretion rate onto SMBHs and SFR is shown to be weak although the average ratio (~10-2) is constant with redshift, effectively shifting the evidence for a co-evolution scenario in a statistical manner to smaller physical scales (i.e., within the same galaxies). The order-of-magnitude increase in this ratio compared to the locally measured value of M BH/M bulge is consistent with an AGN lifetime substantially shorter than that of star formation. Our findings illustrate an intermittent scenario with underlying complexities regarding fueling over vastly different physical (and temporal) scales yet to be firmly determined.