Scott McTominay continued his own mini purple patch for Scotland, netting the opener after just seven minutes of action at Hampden Park.
But despite going behind early on, Spain began to build pressure and threatened Angus Gunn's goal with Joselu leaving the woodwork shaking before half-time.
And the Manchester United midfielder was on hand to convert after brilliant work from Kieran Tierney down the left to make it 2-0 just after the break as Scotland doubled their lead against the favourites.
Steve Clarke's side held on under pressure from Spain, defending bravely, to secure a famous win over the two-time European champions at Hampden Park.