Radamel Falcao had given Atletico the lead inside the opening 10 minutes and the home side went on to dominate for large spells, but Mame Biram Diouf’s goal against the run of play in the lead-up to half-time levelled the score.
Intense pressure from Atleti throughout the second half was rewarded just before full-time when Argentine Salvio curled a superb effort into the top-right corner, giving Diego Simeone’s team the upper hand ahead of the return leg in Germany next week.
It was Atletico’s eighth consecutive win in the competition, and Falcao’s goal was the club’s 400th in Europe.
Atletico started the game on the attack and by the time Falcao had given them the lead in the ninth minute, Simeone’s team had already displayed their threat going forward. When the goal did come it was just as much down to poor defending as it was to the striker’s predatory instincts, as he ran unopposed and glanced a Gabi free-kick past Ron-Robert Zieler in the Hannover goal.
As Atletico continued to press and look likely to add to their opener they were lucky not to gift Hannover a way back into the game after 20 minutes, when Miranda clattered clumsily into the back of Konstantin Rausch.
The hosts almost did double their lead when Falcao got up for a header at the far post after a neat cross from the left by-line courtesy of Arda Turan, but the Colombian’s header – which all packed inside the Vicente Calderon expected him to bury – was just over.
After further forays forward in which Atletico always looked a menace, Hannover equalised in the 38th minute with their first effort on goal. The play spread wide to Lars Stindl on the right and his inch-perfect low cross cut Miranda out of the picture as Diouf slid in behind and put the ball past Thibault Courtois.
Level at the break, Atletico went in wondering how they were not ahead by at least two goals, and they attacked from the outset in the second half. Gabi put the ball across the face of goal, just missing a connection with Falcao, and at the other end Courtois pulled off a fine save to deny Diouf from close range as both sides pushed.
Atletico continued to look the more likely to score however, and as they persisted a sense of frustration crept in, leading to a spate of bookings for the home side. The introduction of Diego from the bench added an injection of further potency to the Atletico attack, and the Brazilian was instrumental in the increasing pressure his side put on their opponents.
As full time approached a long ball forward was cleared only as far as Salvio on the edge of the 18-yard area, and after getting the ball under control and holding off a challenge he sent his spectacular effort in.
There was still time for Diego to draw an excellent save from Zieler with a fantastic overhead kick, as Hannover kept the difference to a single goal having secured an away one of their own.