After a clean sheet for both sides in the first half, Estonian midfielder Konstantin Vassiljev opened the scoring after 61 minutes and just four minutes later striker Vjatseslav Zahovaiko added a second for the hosts.
Snow and icy temperatures are nothing unusual in March in Estonia. There was a light snow shower during the match and temperatures had dropped to minus six Celsius by the final whistle.
"But the conditions were the same for both teams, so we can't make excuses. The Estonians used their chances better," he said.
Estonia agreed to pay €60,000 to bring the Latin Americans to the Baltic state for the two nations' first-ever footballing encounter, Estonian Football Association spokesman Mihkel Uiboleht said.
Estonia are limbering up for next Tuesday's UEFA EURO 2012 qualifier against Serbia in Tallinn. They stand a surprise third in Group C behind leaders Italy and second-ranked Slovenia, and ahead of Northern Ireland, Serbia and last-placed Faroe Islands.