With the tie finely balanced from the first leg in Madrid last week, the game did not open up until after the break when Adrian Lopez spun away from three desperate Hannover challenges to slot home his sixth goal of the competition.
On-loan Manchester United striker Mame Biram Diouf gave the hosts hope as he pulled a goal back with nine minutes remaining, but Atletico sealed their passage into the last four when Radamel Falcao rocketed home a volley from the edge of the area five minutes later.
The German side were undefeated in 20 Bundesliga and Europa League home games so far this season and there appeared little to suggest that statistic would change after a disjointed first half devoid of clear scoring opportunities.
Diouf pulled the hosts' best chance wide on 11 minutes, while at the other end Adrian came closest for Atleti as his header from Diego's cross flashed just over.
The visitors showed more intent to go for the killer away goal after the break and, after Falcao had wasted a similar chance to Diouf's in the first period, Adrian made the breakthrough as he showed great strength and skill to wriggle away from Emanuel Pogatetz before rounding goalkeeper Ron-Robert Zieler and slotting into the empty net.
The Spaniards then seemed set to cruise through to the next round but Diouf put the outcome back in doubt after 81 minutes as he controlled a loose ball inside the area and expertly finished past Thibaut Courtois at his near post.
However, the suspense only lasted for another five minutes as the outstanding Diego played a wonderful pass with the outside of his foot for Falcao to volley home his 28th goal of the season.
Diego Simeone's men now face Valencia in a repeat of their quarter-final clash from two years ago, when Atleti went on to beat Fulham in the final in Hamburg.