A draw would have been enough to send Steven Gerrard's men through to the last 32, but they picked up all three points thanks to Scott Arfield's strike to keep hold of top spot in Group D heading into the final round of fixtures.
Standard twice took the lead in a breathless first half, yet goals from Maxime Lestienne and Duje Cop were cancelled out by Connor Goldson and James Tavernier.
Arfield scored the only goal of a quieter second half to earn all three points for Rangers, who are in the draw for the next round with one group game – away to Lech Poznan – to spare.