That was not even the highest score in this season's competition as two weeks ago Tallinna FC Infonet beat Virtsu Jalgpalliklubi 36-0.
In other matches last month Kuressaare crushed Rapla Lokomotiv 20-0 and Trans Narva battered Eestimaa Kasakad 14-0.
But before anyone suggests the matches must be rigged or fixed for Asian betting syndicates, they should think again.
The Estonian FA sanctions matches between park amateurs and professional top division clubs which lead to the astonishing scorelines.
Estonian FA spokesman Mihkel Uiboleht told Reuters on Wednesday: "The games are above board, no doubt about that.
"We have eight tiers in the country and it was first tier versus the eighth tier, so it is professionals against people who just gather to once or twice a month to play amongst their friends and they might not have a football background."
On June 13 Infonet walloped Virtsu Jalgpalliklubi 36-0, identical to the highest score in British soccer history when Arbroath overwhelmed Bon Accord by the same scoreline in a Scottish Cup game in 1885.
Tuesday's 31-0 scoreline -- with both Sander Sinilaid and Sander Roivassepp scoring nine goals each -- matched the record for an official international when Australia beat American Samoa 31-0 in a World Cup qualifier in 2001.
That match proved the inspiration for a film documentary and a book, both titled 31-0, with the book last month named the football book of the year in the British Sports Book Awards.
Uiboleht said the Estonian FA's principle is that everybody must get a chance to play.
"For the lower teams they get play at big stadiums or they host profession sides at their home ground, and apart from some really big scores there have been a lot of quite competitive matches."
"It is a club and community development idea behind this,"
he added.
(Additional writing by Ed Osmond and Mike Collett; editing by Justin Palmer)
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