In an outing sorely lacking in quality, Portugal were wasteful despite opening the home defence up on numerous occasions.
Scotland themselves had promising opportunities in attacking areas, especially from set pieces, but they did not have the killer edge which could have secured a shock win at Hampden Park.
Scott McTominay and Nuno Mendes went closest in the first half for either team, but the opposing goalkeeper thwarted both of them, and it was Portugal who had the lion's share of the good opportunities after the interval.
Cristiano Ronaldo, who was making his 200th start for the national team, squandered a golden opportunity early in the second period, and shortly after he turned provider for Francisco Conceicao, who scuffed his effort high over the crossbar.
Had Che Adams been slightly more greedy though, he could have headed home a Scotland winner with a quarter of an hour remaining, but he decided to attempt a knock-down which eventually went astray.
Portugal set up camp in the Scotland half for the final 10 minutes, and Ronaldo and Bruno Fernandes will believe they could have won the game for the visitors, but failed to convert gilt-edged chances, and the game ended goalless.
These are the first points Roberto Martinez's men have dropped in the section, and they will still be huge favourites to progress, despite having an off-night this evening, as just one more point in next month's internationals will be enough for them to reach the quarter-finals.
Croatia's inability to hold onto a two-goal lead away in Poland means that Portugal's fate will be decided in their games with those two next month.
This is the first point on the board in Group A1 for Steve Clarke's side after they started with three straight defeats, but they will need to find a win from somewhere next month otherwise they will be heading back immediately to League B.
SCOTLAND VS. PORTUGAL HIGHLIGHTS
Gordon save vs. Portugal (87th min, Scotland 0-0 Portugal)
With the clock ticking towards 90, Craig Gordon made a crucial save to hang on to the point for Scotland, as the 41-year-old denied Fernandes from close range, and most importantly, held onto the ball with Ronaldo lurking.
MAN OF THE MATCH - VITINHA
On a evening that very few will remember, it was tough to pick out a single player for an outstanding individual contribution, but as the visitors dominated proceedings possession-wise, it is fair to single out Vitinha for sticking to his task, keeping the ball moving, and getting Portugal into some good areas throughout the 88 minutes he was on the pitch.
SCOTLAND VS. PORTUGAL MATCH STATS
Possession: Scotland 30% - 70% Portugal
Shots: Scotland 4-15 Portugal
Shots on target: Scotland 2-4 Portugal
Corners: Scotland 1-10 Portugal
Fouls: Scotland 13-19 Portugal
BEST STATS
WHAT NEXT?
Scotland will welcome previous UEFA Nations League finalists Croatia to Hampden Park on matchday five in the middle of November, knowing that a win will keep their destiny regarding relegation in their own hands, while Portugal will host a Poland side that they beat comfortably last week in Warsaw.