Following a 1-0 defeat in the first leg in Germany, Atletico levelled the tie in the 27th minute when Mario Suarez’s strike deflected in off Omer Toprak.
Garcia went closest to a winner for Atletico in extra time but Leverkusen keeper Bernd Leno beat his shot away.
Hakan Calhanoglu, Toprak and Stefan Kiessling all missed for Leverkusen as Atletico won 3-2 in the shoot-out.
lTroy Deeney’s double fired Watford to the top of the Championship courtesy of a 2-0 win at Wigan.
Deeney grabbed the opener in the 54th minute when he headed in a cross from Adlene Guedioura, and the Hornets skipper made the game safe from the penalty spot in stoppage time.
Middlesbrough are second on goal difference thanks to Patrick Bamford’s 16th goal of the season which secured a 1-0 victory at promotion rivals Derby.
Bournemouth, who started the evening on top, slipped to third after a 1-1 draw at Cardiff.
Harry Arter, called into the Republic of Ireland squad for the first time last week, fired them into an early lead with a 25-yard screamer but Bruno Manga powered in a header to equalise in the second half.
Norwich moved up to fourth after a crazy last few seconds at Huddersfield.
Republic of Ireland international Wes Hoolahan had cancelled out Ishmael Miller’s opener but James Vaughan appeared to have won it for Huddersfield with a stoppage-time penalty.
But Vaughan promptly blotted his copybook by getting sent off for his celebration and moments later City’s Jamar Loza popped up with an equaliser to secure a 2-2 draw.
Andre Gray’s late goal kept Brentford in the play-off places as they sank Blackburn 3-2 at Ewood Park.
Ipswich stay a point behind Brentford after Jay Tabb’s scuffed shot bounced through a crowd of players and into the net to sink Bolton 1-0.
ATLETICO MADRID: Moya Rumbo (Oblak 23), Juanfran, Gimenez, Miranda, Gamez, Turan, Koke, Suarez, Calmache (García 45) Mandzukic (Torres 83) Griezmann.
BAYER LEVERKUSEN: Leno, Hilbert, Toprak, Spahic, Nascimento Borges, Bellarabi, Castro, Bender (Papadopoulos), Son Heung-min (Rolfes 77) Calhanoglu Drmic (Kiessling 69).
Referee: Nicola Rizzoli.