We present Spitzer Infrared Spectrograph observations of a complete sample of 57 Sloan Digital Sky Survey type-1 quasars at z ∼ 1. Aromatic features at 6.2 and/or 7.7 μm are detected in about half of the sample and show profiles similar to those seen in normal galaxies at both low and high redshift, indicating a star formation origin for the features. Based on the ratio of aromatic to star formation infrared (SFIR) luminosities for normal star-forming galaxies at z ∼ 1, we have constructed the SFIR luminosity function (LF) of z ∼ 1 quasars. As we found earlier for low-redshift Palomar-Green (PG) quasars, these z ∼ 1 quasars show a flatter SFIR LF than do z ∼ 1 field galaxies, implying the quasar host galaxy population has on average a higher star formation rate (SFR) than the field galaxies do. As measured from their SFIR LF, individual quasar hosts have on average LIRG-level SFRs, which mainly arise in the circumnuclear regions. By comparing with similar measurements of low-redshift PG quasars, we find that the comoving SFIR luminosity density in quasar hosts shows a much larger increase with redshift than that in field galaxies. The behavior is consistent with pure density evolution since the average SFR and the average SFR/BH accretion rate in quasar hosts show little evolution with redshift. For individual quasars, we have found a correlation between the aromatic-based SFR and the luminosity of the nuclear radiation, consistent with predictions of some theoretical models. We propose that type-1 quasars reside in a distinct galaxy population that shows elliptical morphology but that harbors a significant fraction of intermediate-age stars and is experiencing intense circumnuclear star formation.