Rangers hold the lead at the halfway stage of their tie, although it is still all to play for against Luxembourgish outfit Progres Niedercorn after Pedro Caixinha's side only managed a 1-0 win at Ibrox.
Kenny Miller scored the only goal of the game after 37 minutes, leaving Rangers with a job still to do when they travel to Luxembourg for the return leg.
St Johnstone, meanwhile, are on the brink of a first-round exit, having shipped two away goals in a home defeat to FK Trakai of Lithuania.
Trakai held out for the win despite Silenas being sent off eight minutes from time, and they will now be in the driving seat for their home second leg.
The return legs will both take place on Tuesday.