We report new results from the search for neutrinoless double-beta decay in ¹³⁰Te with the CUORE detector. This search benefits from a fourfold increase in exposure, lower trigger thresholds, and analysis improvements relative to our previous results. We observe a background of (1.38 ± 0.07) 10^-2 counts/(keV⋅kg⋅yr) in the 0νββ decay region of interest and, with a total exposure of 372.5 kg⋅yr, we attain a median exclusion sensitivity of 1.7 × 10²⁵ yr. We find no evidence for 0νββ decay and set a 90% credibility interval Bayesian lower limit of 3.2 × 10²⁵ yr on the ¹³⁰Te half-life for this process. In the hypothesis that 0νββ decay is mediated by light Majorana neutrinos, this results in an upper limit on the effective Majorana mass of 75–350 meV, depending on the nuclear matrix elements used.