Goals either side of half-time from Henri Anier and Joel Lindpere earned the hosts their second win in the pool. It doubled their points tally to six while their opponents remain without a single one.
Estonia dominated possession but were restricted to long-range attempts as they struggled to carve out clear-cut chances. The breakthrough arrived in first-half injury time as Anier slotted Konstantin Vassiljev's pass low into the corner.
Andorra had not scored a goal in their opening five qualifiers so their chances of a fightback looked slim - and they got slimmer when Estonia doubled their lead in the 61st minute. Lindpere headed home after Tarmo Kink had nodded the ball back across goal.
From then Estonia had little trouble seeing the game out as their opponents barely mustered an attempt on goal.