Clear-cut chances were few and far between in the Group D encounter as the visitors kept the home side’s much-vaunted attackers largely quiet.
AFP Sport picks out three talking points from the match, which was the 100th competitive meeting between the two historic rivals.
If England are to win their first major tournament since the 1966 World Cup, they will need a fit and firing Harry Kane.
At least that was the thinking before Gareth Southgate’s team kicked off against Croatia at the weekend.
But the captain was largely anonymous in the 1-0 win against the Croats and made little impact against Scotland, substituted with a little over a quarter of an hour to go.
The 27-year old, who won the Golden Boot at the World Cup in Russia three years ago, believes he is a better player now and says he knows when to drop deep and when to attack.
Kane enjoyed a stunning season for his club, winning the Premier League’s Golden Boot for a third time and notching the most assists.
But some pundits have suggested that the forward, at the centre of intense speculation over where he will be playing next season, should focus more on being the focal point of the attack.
He and Southgate both know he must find his touch soon at Euro 2020.
England’s attacking resources are the envy of many teams in the tournament but they have mustered just one goal in 180 minutes of football so far.
The manager made two changes in defence for the Scotland game but kept the rest of his line-up the same, meaning no starting spots for Marcus Rashford or Jack Grealish.
Dortmund forward Jadon Sancho was again deemed surplus to requirements as Southgate stuck with Raheem Sterling, Phil Foden and Mason Mount behind Kane.
England made a bright start but lacked creativity and a cutting edge.
Rashford was a starter not long ago but a combination of injury problems plus the sparkling form of Man City’s Foden has kept him out of the starting eleven.
Southgate, who introduced Grealish and Rashford as second-half substitutes, has a number of game-changing players to call on but England have not clicked yet and must find more fluidity in attack.
Scottish hearts sank when Kieran Tierney was unable to play in Scotland’s opener against the Czech Republic because of a calf injury.
The Arsenal defender was badly missed in Monday’s 2-0 defeat in Glasgow — Scotland’s first match at a major tournament for 23 years.
But at Wembley he was reunited with captain Andy Robertson and the pair were a potent force down the left-hand side.
The two natural left-backs combined to dangerous effect just before the half-hour, with the Liverpool man feeding Tierney.
Tierney surged forward, cutting inside and produced a searching right-footed cross that Stephen O’Donnell met on the volley, only to see his shot saved by Jordan Pickford.
The Arsenal player, notionally playing on the left of a back three, was a constant threat going forward and played his part in a stubborn rearguard performance.