Spurs were always fighting against the odds after that desperate first leg in Madrid put Atletico in complete control of this tie.
But, despite their recent struggles, Igor Tudor's side actually offered up moments of hope as they were willed on by home fans who appreciated the effort and refusal to give up despite a mammoth task.
And this display, coming on top of a deserved league draw at Liverpool on Sunday, drew warm applause at the final whistle despite the disappointment of an exit from the competition.
Spurs deserved their success on the night, showing enough to offer real encouragement as they now tackle the main business of their season – namely staying in the top flight.
And they'll be positive going into Sunday's all-important home meeting with Nottingham Forest, who are only one point behind them in the table along with third-bottom West Ham.
The big opportunity for a miraculous comeback perhaps came when Mathys Tel missed a huge chance to make it 2-0 late in the first half, but he was also one of his side's standout players, a threat throughout.
And what will also give Spurs and Tudor added belief was the manner in which they responded to the setbacks of Atletico's two goals, pushing until the final whistle.
They never gave up, despite the almost certainty of defeat to earn a morale-boosting victory.
It was a far cry from the last time they were here, feeling the full wrath of their own fans after a dismal Premier League defeat by Crystal Palace.
There was genuine appreciation for Spurs' efforts – and that alone will help fuel their battle for survival if they can continue to build on the improvement in their last two games.
