Four-times world champions Italy will qualify if they beat the Czech Republic in Turin, while Germany, bidding for their 16th successive appearance, can follow suit with a win over the Faroe Islands, though a Sweden victory against Kazakhstan would delay the Germans' passage.
The Netherlands, assuming they beat Andorra, will be guaranteed top spot in Group D if Romania fail to beat Turkey.
For other European powerhouses the task is less straightforward.
England will be wary of their trip to Ukraine despite going top of Group H after a 4-0 win over Moldova on Friday. Ukraine warmed up for the potential group decider with a 9-0 hammering of San Marino.
Ukraine are one point behind England, and one of their three remaining ties is against San Marino.
"It's a massive game against Ukraine, but we have nothing to fear and can go there full of confidence," England captain Steven Gerrard, who scored the opener against Moldova, said.
"We need to believe in ourselves, roll our sleeves up and put in a performance, because if we were to get all three points it puts us in the driving seat."
England look more certain qualifiers than France, whose hopes of topping world champions Spain in Group I look forlorn after a 0-0 draw with Georgia on Friday left them three points behind with two games to go.
They must win in Belarus on Tuesday to keep alive any realistic chance of heading the group and avoiding a playoff.
Switzerland fluffed their lines in a dramatic 4-4 home draw with Iceland on Friday and could be vulnerable when they travel to Group E's second-placed side, Norway, on Tuesday.
Victory, and a draw between Iceland and Albania, would be enough to ensure the Swiss will be in Brazil next year.
Russia, who will qualify automatically in 2018 as hosts, will put themselves back in pole position over Portugal in Group F if they win their game in hand at home to Israel on Tuesday.
Italy are renowned for grinding their way through to World Cup finals, having qualified for all but two of the 19 editions of the tournament so far.
They were at it again on Friday with a gritty 1-0 win over Bulgaria, which put them seven points clear in Group B with three matches remaining, starting when they host the Czech Republic in Turin.
The Czechs were stunned by Armenia on Friday, meaning they are now looking at a playoff spot at best, but Italy coach Cesare Prandelli is taking nothing for granted.
"We are one step from the World Cup, but at the moment everything is complicated by our physical condition, which is not optimal," he said. "We will try to recover as much as possible."
Away from Europe, Argentina are on the brink of qualifying as they take on Paraguay on Tuesday needing a win to ensure they finish in the top four of the South American qualifying pool.
Colombia would join them if they avoid defeat in Uruguay.
Costa Rica and the United States will take the first two of three spots from the CONCACAF region with wins over Jamaica and Mexico respectively.
In Asia, Jordan and Uzbekistan play the second leg of their tie to decide which nation gets a final crack at qualifying for Brazil through an inter-continental playoff.
Friday's first leg in Jordan finished 1-1.
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