Celtic progressed to the Champions League third qualifying round after a 2-0 win at Nomme Kalju secured a 7-0 aggregate triumph.
Neil Lennon's side had done most of the hard work at home last week but they triumped again in Tallinn on Tuesday.
The Scottish title winners are now two rounds away from reaching the group stage of the Champions League, having lost to AEK Athens in the third qualifying round last season.
Leigh Griffiths had marked his first start of 2019 by scoring from a free-kick as Ryan Christie inspired Celtic to victory in Glasgow.
And they extended their huge advantage even further in the 10th minute when Aleksandr Kulinits turned into his own net from a low Michael Johnston cross.
Nir Bitton's long-range drive was easily gathered by goalkeeper Pavel Londak as Celtic continued to control the game.
A fizzing strike from Anthony Ralston narrowly cleared the angle of post and crossbar in the 55th minute but, with Celtic not needing to get out of second gear, the tie was already petering out somewhat.
The Estonian side carved out their first clear chance of the game with 13 minutes to go, but substitute Max Mata smashed his shot over the crossbar after springing the offside trap.
And Shved came off the bench to thump home Celtic's second in added time, the striker scoring on first competitive appearance for the club.
Next up for Lennon's men will be Cluj of Romania after they edged out Israeli side Maccabi Tel Aviv 3-2 on aggregate.