Uruguay were already leading 1-0 from a sixth minute Nicolas Lodeiro goal when Jose Quintero was shown a VAR-assisted red card for throwing an arm in an aerial challenge.
The 28-year-old was originally shown a yellow card by referee Anderson Daronco but after the consultation of VAR, Quintero was given his marching orders in Belo Horizonte.
The 23rd minute sending off put Uruguay firmly in the driving seat and Cavani with an acrobatic volley and Suarez with a poacher’s goal made it 3-0 by half-time.
The Uruguayans took their foot off the pedal in an uneventful second half but an own goal from Arturo Mina 12 minutes from time, confirmed by VAR, sealed a miserable night for Ecuador.
"We had our chances in the first half and we took them. That allowed us to manage the game," Cavani said. "They went down to 10 men and that allowed us to control the match."
The result, Uruguay’s biggest win in the Copa America since 1967, puts Uruguay top of the group, with Japan to play Chile in the other Group C match on Monday.
Ecuador, one of only two South American sides never to win the tournament, looked poor throughout the game at the Mineirao stadium and will have to recover quickly before facing Chile, the current Copa America champions in Salvador on Friday.
Uruguay’s next match is against Japan in Porto Alegre on Thursday.