Vetra had three players sent off as Shelbourne won 4-0 and eased through to a second round meeting in the UEFA Intertoto Cup with Danish side BK Odense next weekend.
Trailing 1-0 from the first leg, the tie was all but up for the Lithuanians as early as the third minute when they had central defender Julius Raliukonis dismissed for a professional foul on Glen Crowe.
Despite their numerical advantage Shels struggled in front of goal, however.
Crowe twice, either side of a drilled shot from Joseph Ndo, wasted chances before the lead arrived on 35 minutes when winger Bobby Ryan’s attempted cross ended up in the net for a fluke goal.
Any hope of a Vetra revival ended in first half stoppage time when Rolandas Karcemarskas was sent off for dissent having just been booked for a heavy challenge on Alan Reynolds.
Substitute Jason Byrne headed home Ndo’s 65th minute corner to increase Shels' lead before Vetra had midfielder Robertas Vezevicius sent off for a second booking within a minute.
Crowe added a third goal on 68 minutes, tapping home after Jason Byrne had lobbed keeper Mirza Merlani.
Jason Byrne got his second of the night in stoppage time.
Shelbourne: Delaney; Heary (O‘Halloran, 71 mins.), Hawkins, Dillon, Crawley (J. Byrne, 53 mins.); Ryan, Reynolds, S. Byrne, Cahill; Ndo (Deegan, 71 mins.); Crowe.
FK Vetra: Merlani; Raliukonis, Baikovs, Usaciov, Karcemarskas, Preiksaitis, Vencevicius, Blazys (Litvimas, 78 mins.), Vezevicius, Sernas (Kochanauskas, 90 mins.), Kuznecov (Vaineikis, 87 mins.).
Referee: M. Strombergsson (Sweden).