Sweden have reached the last eight just once since they were runners-up to Brazil on home soil in 1958, while 64 years have passed since Switzerland last graced the quarter-finals of this competition - when they were hosts.
It is Vladimir Petkovic's side who are favourites to come out on top in Tuesday afternoon, with dabblebet offering 13/8 (2.63) for a Swiss success inside 90 minutes.
Janne Andersson's men, though, have confounded their critics time and time again, and dabblebet go 21/10 (3.10) that Sweden win inside normal time in St Petersburg.
This appears to be a very evenly-matched contest and the 2/1 (3.0) quote for extra-time and, potentially, penalty kicks being required to separate these sides could well prove popular with punters.
Defensive duo Fabian Schar and Stephan Lichtsteiner - Switzerland's captain - are both suspended for this tie, so Petkovic will have to shuffle his pack accordingly.
Veteran midfielder Sebastian Larsson, formerly of Sunderland and Hull City, sits out for the Swedes after picking up two yellow cards in his three appearances in Group F.
A tight tussle?
Switzerland have kept a clean sheet in 10 of their last 12 victories and dabblebet offer 5/2 (3.50) that Petkovic's men win to nil on this occasion.
However, Switzerland have not scored in any of their last three knockout stage matches at the World Cup and dabblebet go 8/5 (2.60) that Andersson's men keep a clean sheet.
Sweden have kept a clean sheet in four of their last five competitive outings, including two against Italy in their play-off match.
Four of Switzerland's five goals have come in the second half, while Sweden have, themselves, struck just once before the break in the competition thus far.
With so much at stake for both nations, it would be no surprise to see a cagey opening and dabblebet's 11/10 (2.10) quote for the first half to end goalless could well provide punters with a path to profit.