Esteban Paredes and Eduardo Vargas gave Jorge Sampaoli's Chile the win to recover from a 1-0 defeat against Peru last week and climb up to fourth in the standings - the last automatic qualifying spot for next year's tournament.
Suarez, meanwhile, was lucky to stay on the pitch as he appeared to hit out at the face of Chile defender Gonzalo Jara in the first half.
The referee took no action over that incident, but did book the Liverpool striker for protesting later in the game and he will miss the next qualifying duel against Venezuela as a result.
Paredes, playing in place of the suspended Alexis Sanchez, opened the scoring in the 10th minute and, when as Uruguay looked for an equaliser, Vargas took a loose ball to double the lead in the 77th minute.
Chile goalkeeper Claudio Bravo told Chilevision TV: "We won deservedly. In some moments, we found our best shape. We knew we did not have to make silly fouls. We are very happy for this win.
"We should have won over Peru the other day, but we failed. Now we did and this is a crucial victory."
Ecuador consolidated second position in the CONMEBOL Zone of the Brazil 2014 qualifiers thanks to a convincing 4-1 win over Paraguay at home.
The win helped the Ecuadorians remain second in the standings on 20 points, four below leaders Argentina, who drew 1-1 with Bolivia earlier in the day.
Paraguay, who finished the 2010 World Cup qualifiers on top, surprisingly lie at the bottom of the table on eight points.
Paraguay took the lead in the 14th minute with Luis Caballero opening the scoring from a shot that was deflected by Edgar Benitez on its way to the net, but Felipe Caicedo equalise seven minutes before the break, following a Walter Ayovi free-kick.
The Ecuadorian side started the second half like a hurricane as Jefferson Montero widened the gap in the 50th minute and Cristian Benitez made it 3-1 three minutes later with a header.
With only 15 minutes remaining Benitez consolidated the win with a right-foot strike.
Ecuador boss Reinaldo Rueda said: "We are all shocked by this win, by starting this year in a good way.
"It was not easy at all as Paraguay are a very mature, practical team."
Finally, in Puerto Ordaz, a 13th-minute left-foot strike by Salomon Rondon gave Venezuela a 1-0 triumph over visitors Colombia.
Atletico Madrid striker Radamel Falcao had the chance to level for Colombia at the Estadio CTE Cachamay in the second half, but his right-foot shot hit the crossbar.