For Brighton boss Fabian Hurzeler, it was the perfect evening.
The Lithuanian visitors showed their intent early on by defending deep, camped on the edge of their penalty area in a low block, looking to frustrate the hosts.
Lewis Dunk had scored a stunning 35-yard strike in the 5-0 league win against Coventry, later named as the Premier League goal of the month for September, and the Brighton skipper was unlucky to see a long-range attempt just go over.
But the breakthrough always looked like it would come soon. Hinshelwood had a header tipped over, before Rutter got his first goal of the season to end Zalgiris' resistance.
From then on it was easy for a Brighton side that ended up with nearly 80% of possession.
Hinshelwood, Rutter again and O'Riley added further goals, with the latter denied another by a fine save from away goalkeeper Tomas Svedkauskas.
Hurzeler, speaking to Uefa, said: "It was a very disciplined performance, we kept a clean sheet. A lot of players took their opportunity and that's something we will need for the whole season.
"I always want to emphasise the work we do on and off the pitch to build connections, to build this togetherness; I want to emphasise the work in the shadows, because that's the work we really need to build the connections."
For Brighton, this result continues a superb season in only their second ever continental campaign.
Domestically, they have already beaten Aston Villa 4-0 and embarrassed reigning champions Arsenal 3-0 in the Premier League, and came back from 2-0 down to win 3-2 at Old Trafford and knock Manchester United out of the Carabao Cup.
Hurzeler's side have now scored 29 goals in 10 matches in all competitions and they will fancy their chances of a lengthy run in the Conference League.