Any sort of victory, even on a penalty shootout, will be enough to see Jamie Hamill’s side into the knockout stages.
Since the competition was revamped in 2016 no team from the bottom tier has gone through from the group stage.
But Stranraer are poised to do just that, although fellow League 2 sides Forfar Athletic, Kelty Hearts, Cowdenbeath and Stirling Albion are also still in with a chance of progressing.
The Blues went top of the section on Saturday after beating East Kilbride at Stair Park and stayed there on Tuesday as the other four teams in the group all took points off each other in draws.
Hamill will be on familiar ground at Rugby Park, having made over 200 appearances for Killie over two spells between 2007 and 2016.
But his focus is now on Stranraer – and he seems to have been less than impressed by the pre-match comments of Kilmarnock boss Tommy Wright
He said: “I saw a wee bit from Tommy Wright saying he's looking to take goals off us, so it should be an interesting game.
"We'll not be going there to sit and defend and soak pressure up.
"Tommy Wright has watched us and that's not how we're setting our stall out to play this season.
"I'm happy to go toe to toe with Kilmarnock and see how where we go.
"I know the club inside out. I was there for numerous years and my time at Kilmarnock was very good, I enjoyed every minute. This will be the first time I've been back since my last game there, so I'm looking forward to it.
"But I'm going there as Stranraer manager, hoping to beat Kilmarnock and make a bit of history for a League 2 club by going into the last 16.
"It will be a tough game because Kilmarnock have just been relegated. They've signed some good players, but I've signed some good players as well and it's a game I'm really looking forward to."
Stranraer last made the last 16 of the competition in 2014 when they lost 5-3 to Hibernian at Easter Road.
Even a draw and a penalty shootout defeat might be enough, depending on the outcome of the other group match between Morton and Clyde.