Livingston are slight favourites for the tie given the recent fine form that has taken them to fifth in the Scottish Premiership table, but the Paisley Saints eliminated the mighty Rangers to reach this stage of the competition and they will feel confident.
Livingston head into this game in superb form, having not lost in their last 10 games in all competitions, including eight wins and two draws.
Those draws were in Livi's last two league games, both against Celtic, with the West Lothian outfit drawing 0-0 at Parkhead last weekend and 2-2 at home with the Hoops in midweek.
Ironically enough, Livi's last defeat came at the hands of St Mirren, back in November, when they lost a league game 1-0 at home to Jim Goodwin's team.
They reached the semi-final thanks to a 2-0 home win over Ross County, and the team's supporters must be feeling confident that Martindale, who had to pass a 'fit and proper persons' test to manage the club after being imprisoned in 2006 on drugs and money laundering charges, can inspire the team to emulate the heroes of 2004.
That was when Livi won the League Cup, defeating Hibernian in the final, but first they must deal with St Mirren.
Goodwin's side are currently in eighth place in the Premiership table, a real improvement on earlier in the campaign, though recent results have been somewhat mixed.
In the seven games since they beat Rangers in the quarter-final, the Buddies have only won twice. They have lost twice - to Rangers and Hibernian - and drawn three of those games.
They had a pretty tough route to this stage of the League Cup, getting through a group that contained Partick Thistle and Queen of the South as well as local rivals Greenock Morton.
After the group stage they beat Aberdeen before dispatching Rangers, so Goodwin's team have shown some pretty impressive pedigree in this year's competition.
The Saints have lost just three of their last 17 games in all competitions, and Goodwin knows all about upsetting the odds in League Cup games from his playing days.
Back in 2013 when Goodwin was part of the team that lifted the trophy, they overcame Celtic at the semi-final stage and beat Hearts in the final after being given little chance in either game.
We should be in for a real battle of a game on Sunday in Glasgow.
Livingston Scottish League Cup form: WWWWWW
Livingston form (all competitions): WWWWDD
St Mirren Scottish League Cup form: WDDWWW
St Mirren form (all competitions): LWLDDL
Livingston manager Martindale will not be able to call on South African midfielder Keaghan Jacobs, who has a foot injury that is expected to see him absent until the middle of next month.
Defender Alan Lithgow is also out with a hip injury that is expected to keep him sidelined for around another week or so.
Buddies boss Jim Goodwin has a full squad to pick from, with no injuries or suspensions affecting his plans.
Livingston possible starting lineup:
McCrorie; Fitzwater, Guthrie, Brown; McMillan, Lawson, Pitman, Serrano; Emmanuel-Thomas, Forrest; Hamilton
St Mirren possible starting lineup:
Alnwick; Fraser, McCarthy, Shaughnessy, Tait; Erhahon, Doyle-Hayes, McGrath; Connolly, Brophy, Irwin
We say: Livingston 1-2 St Mirren
This is a very hard game to call, but we think St Mirren will have the League Cup pedigree to take them to a narrow, hard-fought win.
Extra time may well be needed to determine the winner of this one, and it could well come down to an error at a key moment.