Ton looked to have secured a draw when Andy Jackson slotted home to level the scores after Well had earlier fought back from going a goal down to lead 2-1.
But with just four minutes remaining, substitute Gary Smith rose highest to plant a firm header into the net to hand Stuart McCall's side a 3-2 victory.
For Morton boss Allan Moore the outcome was the only negative on a night which he believes provided many positives.
He said: "It was a hard test for us against a good Premier League team - but that's what you want. The only thing I'm disappointed with was the result, but the fact we matched them for 80 minutes was really pleasing.
"We've created some great opportunities, and their keeper has probably had more saves to make than ours.
"But you can't really read too much into these pre-season games. It's when the nitty gritty comes up at Ross County, and the two cup games before that, that it counts."
The visitors started brightly and were just the width of the woodwork away from taking a second-minute lead when Michael Higdon crashed a header against the post.
While Motherwell had the better of the early stages, Morton were creating the better chances and were only denied an opening goal by the goalkeeping heroics of Lee Hollis.
In the 19th minute, the stopper sprung to his left to clutch David O'Brien's curling effort before surpassing that save shortly afterwards by instinctively thrusting out an arm to thwart O'Brien for a second time.
Before the match, Moore told his squad to arrive at the ground earlier than usual for one last run through their set-piece plans.
And this extra preparation paid dividends on the half hour when Andy Graham darted to the front post to volley home Peter Weatherson's precise free-kick to make it 1-0.
But the lead lasted just six minutes, as Jamie Murphy collected the ball on the edge of the Ton box, looked up and curled a sublime effort beyond Colin Stewart's despairing dive to restore parity.
Well ended the half the better of the two sides and could have taken a lead into the break but for a linesman's flag ruling out a Steven Saunders header for offside.
Ton brought on French trialist goalkeeper Florian Verplanck, formerly of AS Monaco, and recent youth signing Creag Little at the interval, while Well rang the changes, replacing all but two players.
Saunders, who was one of those two, continued to prove a real attacking threat - and it was from one of his forays forward from right-back that the Steelmen edged ahead in the 51st minute.
The Scotland internationalist drove to the byline and cut back for the inrushing Jamie Pollock to divert into the net via the post.
It was then Ton's turn to retake the initiative, and O'Brien, Archie Campbell and Michael Tidser all drew strong saves from Hollis.
However, there was little Hollis could do to prevent the Morton equaliser when it arrived in the 73rd minute.
Substitute Darren McGeouch picked out Jackson's run with fine slide-rule pass, and the former St Johnstone man did the rest, rolling the ball beyond the advancing Hollis and into the empty goal.
But just when it looked like the match would end in stalemate, Smith arrived unmarked to nod home Steven Lawless's cross to seal the win.
Well boss McCall said: "Lee Hollis had too much to do in our goal for my liking, but it was a good workout with some good football played."