Uruguay have been forced into a play-off to reach the last three World Cups, winning one and losing one against Australia in 2002 and 2006 respectively, and triumphing against Costa Rica ahead of the 2010 finals in South Africa.
But Uruguayan expectations have changed markedly in recent years, with a run to the semi-finals in South Africa followed by victory in last year's Copa America.
Oscar Tabarez's men now sit third in FIFA's world rankings, and Liverpool striker Suarez believes they must deliver on their billing as the top side in South America and claim the top-four finish that would guarantee them a place at Brazil 2014.
"Our target is to reach a comfortable qualification to the World Cup," Suarez said.
"Despite all the achievements we managed in the last few years, we can't forget we suffered a lot to qualify for our last two World Cups."
Uruguay lead the way in the South American qualifying zone with seven points from their first three games, just ahead Argentina and Venezuela on goal difference with both those sides having played one game more.
Third-placed Venezuela provide Uruguay's opposition in Montevideo on Saturday, with the visitors looking for a good result to boost their hopes of reaching their first ever World Cup finals.
Certainly history in on the side of Cesar Farias' men, who have gone 12 years without tasting defeat at the hands of the Uruguayans.
"Venezuelan football improved a lot and they surely will be hard rivals for us," added Suarez, who will form part of a potent three-man attack alongside Diego Forlan and Edinson Cavani.
Second-placed Argentina will bid to overhaul Uruguay at the summit when they host Ecuador in Buenos Aires.
All eyes will be on Argentina forward Lionel Messi to see if he can replicate for the national team a little of the form that saw him score a record 73 goals in all competitions for Barcelona last season.
Messi - who will captain the side on Saturday night - will be partnered in attack alongside Manchester City's Sergio Aguero, with coach Alejandro Sabella reportedly unsure whether to throw Real Madrid frontman Gonzalo Higuain into the mix as well, or err on the side of caution and select Metalist Kharkiv's Jose Sosa as an extra body in midfield.
Certainly Aguero's club and country team-mate Pablo Zabaleta believes the coach should make full use of the enviable array of firepower at his disposal.
"To have Leo, Kun [Aguero] and Pipa [Higuain] gives us a maximum security," he said.
"If they have a good day, our rivals have no chance."
Ecuador coach Reinaldo Rueda will field a lone forward in the form of Christian Benitez and admits his side - despite winning two of their opening three qualifiers - will need a perfect performance to take anything from the match.
"We have to be clever and try to keep the ball," he said.
"The truth is that against players like the Argentinians, we can't commit any mistakes."
Also on Saturday, bottom side Bolivia go in search of their first win when they host Chile, who have picked up six points from their first four matches.
At 3,600 metres above sea level, the Bolivian capital La Paz will as always pose a unique test for the visiting side, and Chile have prepared for the game with a five-day acclimatisation in the Andean city of Calama.
But Bolivia coach Gustavo Quinteros has moved to play down the altitude issue ahead of the game as he bids to improve his side's record of just one point from their first four games.
"I think the altitude will not be crucial," he said.
"If we win, it will be because of our players and not the height."
On Sunday, Jose Pekerman takes charge of Colombia for the first time when the Cafeteros face Peru in Lima.
Colombia sit in sixth place with four points from three matches - a sequence that resulted in the dismissal of Pekerman's predecessor Leonel Alvarez - and Colombia defender Mario Yepes has backed the new man to improve the side's fortunes.
"Pekerman has a simple and clear message," the AC Milan player said.
"I think we can complete a good campaign with him, even though the South American qualifiers are the hardest in the world."
Paraguay are the only member of the nine-team qualifying zone not in action this weekend.
They resume their campaign against Bolivia June 9.