Former finalists England, who played their one final when they won the title in 1966, and Sweden, who lost to Brazil on home soil in the 1958 final, are still in the half of the draw vacated by the 2010 champions after their loss to the hosts.
The odds on England winning the World Cup for a second time were immediately cut from 6-1 to 5-1 after Russia's victory, making them third favourites behind France and Brazil with bookmaker William Hill.
Croatia's victory over Denmark in another penalty shootout later on Sunday kept them alive in the same section of the draw and saw England's odds drift slightly to 11-2.
The Croatians, whose best previous showing was a trip to the semi-finals in 1998, were also listed at 11-2 despite a much less impressive performance in Nizhny Novgorod than in their earlier group matches.
Russia will take on Croatia in Sochi on Saturday, hoping to continue to benefit from the hosts' dividend to better the single semi-final appearance that the Soviet Union achieved in 1966.
Switzerland, who have never done better than the spot in the last eight they achieved as hosts in 1954, take on the Swedes on Tuesday in St Petersburg with the winners going on to face England or Colombia.
Colombia, whose best finish was their run to the quarter-finals in Brazil four years ago, take on the English in the last round-of-16 match later the same night in Moscow.
The last addition to the elite group of 12 nations who have contested World Cup finals was Spain when they won the title for the first time in 2010.
France, the 1998 winners, beat Argentina to reach the quarter-finals on Saturday and are in the other half of the draw with fellow former champions Brazil and Uruguay, the three nations having competed in 11 finals between them.
Latest odds on winners of 2018 World Cup:
7-2 France, Brazil
11-2 England, Croatia
6-1 Belgium
14-1 Uruguay
16-1 Colombia
20-1 Russia
33-1 Switzerland
40-1 Sweden
50-1 Mexico
200-1 Japan
(Source: William Hill)
(Writing by Nick Mulvenney in Kazan, editing by Clare Fallon)
