A scan of the League Cup fixture card might have highlighted this tie as one with the potential for an upset but there was to be no giant-killing act in Greenock.
Kris Doolan's goal on the stroke of half-time was all that separated Thistle and Morton at Cappielow, but it was enough for Alan Archibald's side. The Firhill club will take their place in the third round draw when it is made today.
There will be more important battles to be fought for Thistle this season but a cup run would still be a welcome addition to their campaign, with and the first hurdle negotiated safely last night against familiar foes.
The fortunes of these two clubs have contrasted significantly since their last meeting in the First Division two seasons ago, with Thistle now setting their sights on a place in the SPFL Premiership top six and Morton looking to bounce back to the second tier under new manager Jim Duffy.
Such a gap not always evident last night, however, as the visitors were unable to hammer home their superiority in a competitive affair. Indeed, after turning in a low-key performance against Hamilton Academical at the weekend as they suffered their first league defeat this season, Archibald's side had a point to prove at Cappielow.
However, Thistle struggled to find their stride, a couple of strikes from Steven Lawless and a Conrad Balatoni header the most they could muster early on as they struggled to find any rhythm in the final third.
Cup success is hardly the priority for the Morton this term either, as they bid for the League 1 crown. Yet they would still have fancied their chances of taking a scalp as they competed well against Thistle.
If you are to upset the odds, though, then you have to take your chances when they come along and that was to prove the the Greenock side's downfall - with Stefan McCluskey the main culprit. Either side of the break, the striker should have scored but he first headed wide from a Reece Hands free-kick and then, with only Paul Gallacher to beat, put a shot wide after capitalising on a Balatoni error.
In between, Doolan had shown the Morton striker how it should be done. The Firhill forward had seen just 30 minutes of action before the trip to Greenock last night but marked his first start of the campaign with a goal; a neat touch and clinical finish giving his side the lead on the stroke of half-time.
It was an advantage which should have been doubled just after the restart, when Kallum Higginbotham collected Stephen O'Donnell's cross. However, Nicolas Caraux pulled off a superb point-blank save to keep Morton in the tie.
After spurning two glorious chances, McCluskey was left frustrated for a third time and with just 20 minutes remaining - the former Clyde forward being booked for diving by referee Stephen Finnie.
It was a decision which infuriated the hom supporters but Gallacher was equally unhappy, squaring up to McCluskey after the Morton man nipped on to a Declan McManus header and went to ground.
With that, Morton's chances also crumpled. Instead it was Thistle that took the plaudits and a place in the next round.