Aberdeen, Dundee United and Hibernian, along with Celtic and Rangers, had received byes to the second round because of their participation in European competitions.
The Dons have been drawn away to Championship side Greenock Morton, while United and Hibs will visit Premiership opposition in the shape of Kilmarnock and promoted Livingston respectively.
Relegated St Johnstone host top-flight Motherwell in the remaining tie, with matches to be played on the weekend of 16/17 August.
The full fixture list and TV selections will be confirmed at the end of the week following the Uefa second-round qualifying matches.
St Mirren manager Stephen Robinson told BBC Radio Scotland’s Sportscene: “First and foremost, you try to progress to the knock-out stages and try to get a home tie – and we’ve done that.
“Of course, you can get an easier tie than Hearts – they are spending millions of pounds and it’s a huge football club with expectations – but we fancy anybody here.”
As for Ayr’s trip to Firhill, manager Scott Brown added: “We can’t get away from Partick Thistle. We might as well play them again.
“We would have loved a home draw, but we have come away to a top-six side and competed and, especially in the second half, we were miles better than them.”
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