Bolivia goalkeeper Carlos Lampe scored an unlucky own goal to open the scoring but at times almost single-handedly kept his side in the game.
Even so, Bolivia will be the first side eliminated from the Copa if Paraguay avoided defeat against Chile in the late Group A match.
Uruguay thoroughly deserved their first win of this year’s tournament as they dominated throughout.
They could even yet win the group, currently led by Argentina, if other results go their way.
The first clear sight of goal fell to Uruguay’s Giorgian De Arrascaeta, but after shifting the ball onto his left foot he blazed it well over the bar from 20 yards.
Two minutes later Bolivia’s Rodrigo Ramallo got behind the Uruguayan backline but fizzed a shot inches wide from an angle.
Uruguay’s Luis Suarez was next to garner a sight of goal but Lampe was out quickly to smother his effort.
On 20 minutes a long ball over the top left star players Cavani and Suarez — the two most prolific forwards in Uruguay’s history — with a two-on-one situation.
But the veteran pair somehow contrived to make a mess of it, delaying shooting opportunities and allowing Lampe to come out and swat the ball off Cavani’s toes.
Cavani was later denied by a last ditch tackle, while Suarez sent a header into the side netting 10 minutes from halftime.
The pair were a constant menace to the Bolivia backline, though, and their pressure resulted in the opening goal.
De Arrascaeta crossed from the right and a sliding Jairo Quinteros, in trying to prevent either of the veteran forwards converting a simple tap-in, deflected the ball off Lampe and into his own net.
There was still time before the break for Lampe to plunge to his left to keep out a Suarez freekick.
Lampe started the second half the way he ended the first, denying Cavani from seven yards with a reaction block.
His opposite number, Fernando Muslera was not a complete spectator and had to tip a long-range strike from Ramiro Vaca over the bar.
But Lampe was soon back in the thick of things, tipping a fierce drive from Rodrigo Betancur over the woodwork.
Suarez tried to chip Lampe from long range while Cavani headed over from 12 yards as Uruguay continued to push for a second goal.
Substitute Facundo Torres was next to miss, shooting wide after he was picked out by Federico Valverde’s deep cross from the right.
Manchester United’s Cavani finally ended Bolivia’s resistance 11 minutes from time, converting a cross from the lively Torres, whose cameo saw him also send another shot just wide.