The Swedish outfit are struggling domestically but they put their recent poor form behind them with a resounding away win in Tallinn
It was a bad night for Estonia in the Europa League, as Trans were trounced 3-0 at home by Gefle, while Bala Town recorded a shock 1-0 win over Levadia.
Gefle, who are currently 12th in their domestic league, defied a run of form that had seen them fail to triumph in any of their previous 11 games with an impressive away victory in the first leg of their first-round qualifier in Tallinn.
Trans, who sit sixth in the top Estonian division, gave their opponents the lift they needed just two minutes before half-time. Aleksandr Dubokin's own goal just before the break gave Gefle the advantage and it was one they doubled 12 minutes into the second half.
Sweden international Mikael Dahlberg scored the important second goal, with the strike his first in more than two months. Midfielder Jonas Lantto sealed Gefle's win with another strike in second-half stoppage time.
Welsh outfit Bala Town claimed a surprise 1-0 home win over Levadia, who are also of Estonia.
Levadia sit first in the Estonian top-flight but were stunned by Bala, as the Welsh Premier League side extended their winning streak to 13 matches.
Englishman Ian Sheridan scored the game's only goal after four minutes and his side held firm in the closing stages to claim a memorable win.
Other first leg results saw Qarabag of Azerbaijan win 1-0 at Macedonian club Metalurg Skopje, thanks to a second-half strike from Brazilian Reynaldo.
Maltese outfit Sliema Wanderers came from behind to draw 1-1 with Khazar Lankaran of Azerbaijan, who were reduced to 10 men when Elnur Allahverdiyev was shown a second yellow card eight minutes from time. Nigerian Stanley Ohawuchi cancelled out Nildo's early strike to give Sliema a draw.
The second legs will all be played on July 11.