In an enthralling clash at Wembley Stadium, both sides squandered big chances and will feel like they'd done enough to earn all three points.
The England centre-half rose highest from a corner just after the ten-minute mark but his powerful header came crashing back off the post rather than nestling into the corner of David Marshall’s net.
That chance sprung the hosts to life, and Sterling did his best to keep that momentum going when he picked the pocket of Scott McTominay and squared for the onrushing Mason Mount.
However, the Chelsea midfielder couldn’t divert his effort on target, flashing an instinctive finish wide of the near post.
The visitors were next to go close, Stephen O’Donnell forcing a smart save from Jordan Pickford on the half hour courtesy of a vicious low volley back across goal from a looping cross.
A full-blooded encounter remained scoreless despite the best efforts of both sides, who were just lacking quality in the final third of a rain-sodden Wembley turf.
The first proper chance of the second 45 fell to Scotland’s Lyndon Dykes, who’s goal bound effort was expertly cleared off the line by Chelsea’s Reece James just after the hour.
Gareth Southgate’s side continued to try and exploit a chink in the Scottish armour, and finally found space in behind when Luke Shaw wriggled his way in from the left wing.
But another chance went begging, as the the full-back shanked his attempted trivela effort high and wide of the far post.
And it was Scotland’s turn to have their head in their hands with 15 to play, Che Adams blazing a good chance over the bar when he floated into a dangerous area from Andy Robertson’s searching ball.
As the game ticked past 90 minutes, there was just enough time for a final chance, as Declan Rice and Sterling did their best to bundle the ball home from close-range, but the ensuing goalmouth scramble would only yield a visiting free-kick.
England have to wait until Tuesday’s clash with the Czech Republic to guarantee their spot in the last-16, while Scotland’s hopes of reaching the knockout stages of a major tournament for the first time remain in the balance ahead of their clash with Croatia.
The Three Lions sit second on four points, behind Tuesday’s opponents by virtue of goal difference, while Scotland remain rooted to the foot of Group D with a solitary point.