It was expected to be a tough encounter but Óscar Tabárez’s men easily blew out their opponents without ease in surprising fashion.
Cavani, who scored for Manchester United against Everton last weekend, got the opener for Uruguay in the fifth minute after Nahitan Nandez had done the hard work in midfield by robbing the ball and setting him up to fire home a low right-foot shot.
Suarez then added to the lead nine minutes into the second period when he scored from the spot after Jeison Murillo brought down Rodrigo Bentancur.
Darwin Nunez completed the scoring after 73 minutes when his pot shot from 25 metres beat the diving David Ospina.
Yerry Mina was sent off for Colombia after a second yellow card in the final minute of the game to complete a miserable afternoon for the home side.
Suarez’s goal was his 63rd international strike and came after he scored twice from the penalty spot in Uruguay’s 4-2 loss to Ecuador and once in their 2-1 win over Chile in their opening qualifier last month.
The victory takes Uruguay to six points after three games, while Colombia, who beat Venezuela and drew away to Chile in their first two games, have four.
The top four sides in the 10-team South American group qualify automatically for the Qatar 2022 finals and the fifth-placed team go into an inter-regional play-off.
Uruguay now travel home to face Brazil on Tuesday when Colombia will be away to Ecuador.