Unfortunately for them - now unbeaten in five matches - every time they pull off a result like this draw away to the league leaders, their closest rivals for relegation, Cowdenbeath, always seem to go one better.
As for Falkirk, it seems as though none of the three title challengers really feel comfortable peering down at the rest of the league. Hamilton and Dundee have both stood perched on top recently before slipping off, but this wobble was not quite so painful - especially after the stadium announcer corrected the other SPFL Championship scores at full-time.
"Actually, there's been a late goal, it's now Dundee one, Alloa one," he boomed out to the day's biggest cheer. The match was a tale of three Falkirk penalties - two given, one not; one scored, one missed - and a brilliant strike by Dougie Imrie. And indeed, if the mercurial playmaker had shown just a little composure he might have won it on the break when Falkirk were chasing a winner.
The first penalty came not long before half-time. An innocuous high ball was floated to the back post when Steven Roberts idiotically pushed Conor McGrandles. Derek Gaston, though, pulled off a brilliant double save from Rory Loy, back up on his feet quickly to stop the striker's second stab. It was Loy's second miss in two weeks; when another spot kick was later won, it was not he who stepped up. "I don't care who takes them," insisted Gary Holt, the Falkirk manager. "I only took one in my career and I missed it. You've got to have big cajones to stand up and take it. Whoever wants to can take them."
Instead, it was Morton who went in front minutes later. They were defending when the ball was hoofed up the park towards Imrie, who seemingly had nowhere to go before a deft flick left him behind the entire home defence. Garry O'Connor set off down the right flank, where Imrie's curled pass found him puffing and trundling. But while this expanded, director's cut edition of the former Hibs striker may not be remotely mobile, he was able to return the ball to Imrie, who with a pretty dink over Michael McGovern evened the scores.
In the end, both managers were satisfied, though not without their grumblings. Holt pointed to a third penalty appeal from McGrandles and David Hopkin, the Morton assistant manager, agreed with Holt that the second had probably been soft, Craig Sibbald getting in front of Fouad Bachirou and tumbling to win it.
But, for the most part, Morton looked good, with the on-loan McKay quick and clever, and showing enough deftness and vision to make you wonder why Rangers were not using him cheaply at a lower level.
"We've got to concentrate on our own thing," said a pleased Hopkin. "We're going in the right direction."
It's just a shame that everyone else has a head start. And is just as quick.