Mountainous minnows Andorra had rarely tasted success at this or any level, but were seconds away from equalling their biggest ever win - a 1-0 victory against Lithuania three years ago - after St Johnstone’s Jason Kerr gave away a penalty, which was converted by Ricard Fernandez.
But Morgan struck in injury time to rescue a point for the Scots, whose own qualification hopes are surely all but over with four tough games left including visits to Holland and Ukraine and a visit from England.
And manager Scot Gemmill admitted he was disappointed with the level of intensity from his players.
He said: “There were no surprises for us. We knew it would be very hard for us to create chances against Andorra, it’s a very narrow pitch and it wasn’t in good condition.
“Previous Andorra performances have shown they are hard to break down - England only scored one goal here. We weren’t surprised by the type of game we had here, but at the same time we are disappointed with our performance.
“The players had to step up to the plate and match our better that resilience and fight that the Andorran team showed and too many times we didn’t do that.
“In terms of when we didn’t have the ball, the intensity was not there. Too many times we didn’t win the first header, the knock down, the tackle, all the things that you need if you want to produce a good performance. Andorra were too often first to the ball. Undoubtedly, we had to do more.
“Of course we want to do everything we can in terms of qualification, but we need to play every game at the highest level and tonight we haven’t done that.”
Scotland were of course missing regulars Scott McKenna and Oliver McBurnie - both of whom started for Alex McLeish’s side against Costa Rica, but they still had their most expensive player Oliver Burke - who looks more and more downbeat and isolated in every appearance - as well as the likes of John Souttar and Rangers’ Greg Docherty.
You would have expected Scotland to dominate, but it took them almost half an hour to get a shot of any description and the Andorrans had missed plenty of chances before then.
Kerr should have volleyed Scotland in front, but he was guilty of giving away a 77th minute penalty after he tugged Alex Martinez in the box. Ricard Fernandez converted the spot kick.
But just when it seemed certain Scotland were set to suffer complete ignominy in the Pyrenees Principality, Morgan drilled home a low show that was deflected on its way into the net to rescue a point and save Scotland from disgrace.
ANDORRA (4-5-1) Alvarez; De Pablos, Garcia, Llovera, Pomeras; Bove, Reyes, Di Castillo, Cervos, Fernandez; Martinez.
UNUSED SUBS: Siverio, Robelo, Guellin, Bove, Armada, Tizon.
SCOTLAND (4-1-4-1): Fulton: Cadden, Souttar, Kerr, Taylor; Campbell; Burke, Docherty (Brophy 53), Mallan (Smith 61), Morgan: Hardie.
UNUSED SUBS: R Doohan, Burt, Muirhead. St Clair, Wright.
BOOKED: Souttar, Smith