Rovers crossed the line to Windsor Park and planted their flag with three goals in the first 30 minutes.
Strikes from Joshua Honohan and Jonny Kenny and an own goal from Thomas Cosgrove put the League of Ireland champions in control and Graham Burke killed off the game in the second half after Christopher Gallagher scored for Larne.
It was a good performance for Rovers who put some early points on the board in the league phase of the revamped third-tier competition.
Larne have been taught a harsh lesson as they remain winless in their opening two games in what is the NIFL Premiership champions’ first attempt at a group stage European competition.
They may have been hurt by the game being played at an almost empty Windsor Park rather than their usual home of Inver Park and fell behind in just the third minute when Honohan converted at the far post.
Rovers doubled their lead in the 24th minute when Kenny headed home Burke’s cross and the play was so good that Cosgrove scored an own goal six minutes later, the goal surviving a VAR review.
Gallagher gave the home side some hope early in the second half when he burst from the edge of the area.
However, this was short-lived as Burke made it 4-1 six minutes later when he found the bottom corner after a good run.