The Tartan Army clinched a point against Denmark after withstanding pressure from the hosts, and had key moments to take all three points themselves.
Both sides ultimately lacked the clinical edge which cost them the three points.
Against the highest quality opposition in the group, a point was more than satisfactory for Scotland, who go to Greece on Monday.
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Story of the Match
The Danes have featured in the last two World Cup s in Russia and Qatar, and Brian Riemer made three alterations from the side that kept a clean sheet against Lithuania in the summer.
Barcelona's Andreas Christensen took the place of Jannik Vestergaard, while Joakim Maehle was given the nod ahead of Manchester United's Patrick Dorgu on the left.
Brentford's talisman Mikkel Damsgaard was favoured over Christian Eriksen in the midfield.
Steve Clarke opted for seven changes from their rout in a friendly against Liechtenstein in June as he hopes to round off his tenure with the coveted World Cup qualification.
Among those was Nottingham Forest's new signing, Angus Gunn, ahead of Ross Doohan, reinstating a more experienced name between the sticks.
Brentford's Aaron Hickey started at right-back after almost two years out of action due to injury.
Meanwhile, Ballon d'Or nominee Scott McTominay was chosen to start alongside Bologna midfielder Lewis Ferguson.
Action gets underway in Copenhagen
It was one-way traffic from word go at the Parken Stadium in Copenhagen as Denmark commanded possession. Scotland were unable to retain the ball once they retrieved it, yet the incessant pressure from the hosts failed to convert to clear-cut opportunities early on.
Scotland did muster some chances once they managed to string passes together and earned their first corner inside 20 minutes. Aston Villa stalwart John McGinn peeled off at the back post but lacked the clinical edge to go for goal.
Ryan Christie proved his worth once he executed a dangerous cross into the area, targeting a scampering Che Adams. Yet, the striker was not on the same page and arrived too late to meet the delivery.
Denmark showed flashes of intent when Monaco marksman Mika Biereth was threaded through, but the striker was unable to reach the pass.
Approaching the interval, McGinn was involved in the attack once more. His delivery met Ryan Christie whose tame headed effort continued to keep Celtic goalkeeper Kasper Schmeichel quiet for the half.
Despite his anonymity for much of the first half, Scott McTominay surged forward powerfully beyond the Danish defenders and his ball fell to the feet of McGuinn. Maehle anticipated his shot and made a timely intervention to prevent a potential opener in the contest.
McTominay glided past his defender again after some neat footwork and forced Schmeichel into action, and turned down an option to lay off a teammate.
Denmark captain Pierre-Emile Hojbjerg was then a whisker away from nestling his effort inside Gunn's left post as he attempted to galvanise the home support.
Both sides were ramping up their pursuits for the goal to break the deadlock. Adams found his striking partner, Lyndon Dykes, who delayed his strike too long, and the recovering Danish defence comfortably thwarted his shot.
Scotland almost suffered a major blow to their chances of taking something away from Copenhagen when the referee was sent to review a handball committed by substitute Max Johnston. He denied VAR's claims that Johnston's touch warranted a red card, and he stuck by his original decision.
Scotland chase a late winner
The visitors were searching for a winner to snatch all three points as Steve Clarke made a triple attacking change. Teenager Ben Doak rifled towards Schmeichel's goal, and a deflection sent his shot behind for a corner.
Rasmus Hojlund had been left on the bench by his manager but made an instant impact after his introduction. Gunn stood firm at close range to keep his side's hopes for a point intact, despite Hojlund straying offside.
Denmark finished with a late onslaught, but Scotland's defence had been convincing throughout, and their final defensive actions epitomised their resolve to earn them a valuable point.
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Player of the match - John McGinn
Someone who sets the tone for any positive performance at domestic level and no doubt when representing his nation.
Although he lacked conviction when foraying into attacking areas, his persistence caused headaches for the established Danish defenders, and he created threatening chances.
Undoubtedly, he is Steve Clarke's most reliable player, and he is capable of holding his own against opponents like Denmark.
