Last year's league and cup winner FC Levadia failed to win in the first round, managing only a 0-0 draw with ambitious FC Infonet.
Sillamäe Kalev, last year's runner up, beat Paide Linnameeskond 4-1, while FC Flora, third in 2014, beat newcomer Viljandi Tulevik 3-0.
Nõmme Kalju and Narva Trans also recorded big wins, beating Tartu Tammeka 3-0 and Pärnu Linnameeskond 5-2 respectively.
Infonet, who recently beat Levadia to sign Estonian national team midfielder Aleksandr Dmitrijev, will host Flora on Friday. Kalju travels to Paide, Sillamäe to Viljandi and Levadia hosts Narva Trans in the second round.
Editor: J.M. Laats