Andres Oper finally got Estonia off the mark in FIFA World Cup qualifying Group D, but Andorra have now gone 13 games without a goal since a 2-1 friendly loss to Moldova in February 2011.
Estonia had not registered in three Group D fixtures until Oper chested the ball down for Martin Vunk on 57 minutes, and slotted a loose ball into the unguarded net for his 38th international strike after his team-mate's effort clattered against the post.
Andorra made a bright enough start at the Estadi Comunal and did their best to press their opponents, but were soon on the back foot, with Ats Purje and Oper both heading crosses from the left over the bar. Giant Estonia forward Tarmo Neemelo was given precious little room for manoeuvre, though chances kept coming the visitors' way, with Purje flashing one wide from distance and Joel Lindpere squandering an even better opportunity just before the break.
Tarmo Rüütli's side nearly paid for their profligacy soon after the restart, with Sergei Pareiko producing a fingertip stop to fend away Victor Moreira's speculative effort from 40 metres, yet that strike from Estonia's all-time top scorer settled their nerves. Andorra were to carve out some chances in the closing minutes but could not prevent a tenth successive defeat against their Baltic guests.