Cavani got the opener 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.
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.