By solving the two-active-electron time-dependent Schr\odinger equation in an intense, ultrashort laser field, we investigate evidence of electron correlations in the high-order harmonic generation spectrum of helium. As the frequency of the driving laser pulse varies from 4.6 to 6.6 eV, the 13th, 11th, and 9th harmonics sequentially become resonant with the transition between the ground state and the isolated $2s2p({}^{1}P)$ autoionizing state of helium, which dramatically enhances these harmonics and changes their profiles. When each of the 9th and 13th harmonics are in resonance with this autoionizing state, there is also a low-order multiphoton resonance with a Rydberg state, resulting in a particularly large enhancement of these harmonics relative to neighboring harmonics. When the 11th harmonic is in resonance with the $2s2p({}^{1}P)$ autoionizing state, the 13th harmonic is simultaneously in resonance with numerous higher-energy autoionizing states, resulting in a competition between these two harmonics for intensity. These results demonstrate that even electron correlations occurring over a narrow energy interval can have a significant effect on strong-field processes such as harmonic generation.