In the final group game, Manchester United forward Cavani's goal moved Uruguay up from fourth to second position, avoiding a last-16 meeting with hosts and defending champions Brazil.
Paraguay came into the contest hoping to claim its first Copa win against Uruguay since 1947, with an outside chance of topping Group A, but instead slipped to third and will next face Peru.
To make matters worse for La Albirroja, influential Paraguay midfielder Miguel Almiron limped off, placing his quarter-final availability in doubt.
Uruguay needed to avoid defeat to ensure they would not face Group B winners Brazil in the quarters and started with intent as Cavani headed wide in the third minute, while team-mate Giorgian De Arrascaeta grazed the post moments later.
La Celeste won a penalty following a clumsy challenge from Angel Romero as Cavani emphatically hammered the spot-kick past Paraguay goalkeeper Antony Silva.
Uruguay continued to dominate as Nicolas De La Cruz went on a superb run, beating two opponents, before laying off for Cavani, whose dangerous cutback across goal was cleared by Omar Alderete.
Almiron went off injured on the half-hour mark, before Uruguay thought they had a second via Matias Vecino, although it was disallowed with Cavani offside in the build-up.
Paraguay had a goal disallowed early in the second half too, when an offside Oscar Romero nodded home.
Luis Suarez replaced Cavani in the 68th minute and should have made it 2-0 when he broke clear alongside Rodrigo Bentancur but the pair got their wires crossed.