Tallinn scored 33 of their points from beyond the three-point line and a further 23 points from free throws as they overcame a 41-37 half-time Guildford lead.
The Estonian champions, who supplied all but one of the players for their national squad in the summer's Olympic Games, relied totally on their shooters, led by Aivar Kuusma, as they surrendered 25 offensive rebounds to the English champions.
But Guildford, perhaps predictably on the away leg, fell foul of the officials. Martin Henlan, their 6ft 10in centre, was on four fouls and one further offence away from banishment with only seven minutes of the second half played.
The aggression of the 6ft 9in Trevor Gordon and the guard Karl Brown also brought them to the four-foul mark more quickly than the coach Kevin Cadle would have liked, leaving Tallinn to reap a rich harvest of 23 free throws out of 31 attempts.
Derek Thompkins, one of two new Americans in the Guildford line-up, led their scorers with 20 points but fouled out in the final minute.
Gordon, with 18 points, and the American Tyrone Shoulders, with 11, led the Kings' close-range assault on Tallinn's basket.
Next week's return has to be played at Crystal Palace as the Kings new home at the 3,000-seat Guildford Spectrum will not be ready until next month. A six- point win for Guildford will earn a second-round tie with the French club, Limoges.
MEN'S EUROPEAN CLUBS' CHAMPIONSHIP First preliminary round (Tallinn): Kalev Tallinn (Estonia) 80 Guildford Kings (England) 75.Reuse content