A scan down the League Cup fixture card could have seen this game circled as a one to watch in terms of an upset, but there was to be no giant-killing 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, who will take their place in the third-round draw today.
There will be more important battles to be fought for the Jags this season, but a cup run would be a welcome addition to their CV and the first hurdle was negotiated safely against familiar old foes.
The fortunes of these two have contrasted significantly since their last meeting in the First Division two seasons ago, with Thistle now setting their sights on the Premiership top six and Morton looking to bounce back to the second tier under boss Jim Duffy.
The two-division gap was not always evident last night, however, as the Jags didn't hammer home their superiority in a competitive affair.
After turning in a low-key performance against Hamilton at the weekend as they suffered their first Premiership defeat, Archibald's side had a point to prove at Cappielow.
But Thistle once again failed 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 far from the top priority for the Ton this term as they bid for the League One crown, but they would have fancied their chances of taking a scalp as they did well against a strong Thistle side.
If you are to upset the odds, you have to take your chances when they come along and that was to prove the Ton's downfall, with striker Stefan McCluskey their main culprit.
He should have hit the net either side of the break, but first he headed wide from a Reece Hands free-kick and then, with only Jags keeper Paul Gallacher to beat, he put his shot wide after capitalising on a Balatoni error.
In between, Doolan had shown how it should be done. The Firhill forward had seen just 30 minutes of action before the trip to Greenock but marked his first start of the campaign with a goal, a neat touch and clinical finish giving Archibald's side the lead on the stroke of half-time.
It was an advantage that should have been doubled just after the restart when Kallum Higginbotham collected a Stephen O'Donnell cross but keeper Nicolas Caraux pulled off a superb point-blank save to keep Morton in it.
After spurning two glorious chances, McCluskey was left frustrated for a third time of the night 20 minutes from time when the former Clyde star was booked for diving in the box by ref Stephen Finnie.
It was a call that infuriated the Ton faithful, but Gallacher was equally as unhappy, the two squaring up after McCluskey went to ground as he tried to get on the end of a Declan McManus header.
And, with that, Morton's chance was gone. Duffy and his side can take the positives, but it was Thistle who took the plaudits and a place in the hat.