Steven Whittaker and Madjid Bougherra were both shown straight red cards for the visitors, before Malmo’s Ricardinho was also dismissed by Russian referee Vladislav Bezborodov on a night of high drama at the Swedbank stadium.
Nikica Jelavic cancelled out Daniel Larsson’s strike from last week’s clash in Glasgow but it was Jiloan Hamad who had the final say with a late goal to send the home side through.
Rangers must now settle for a Europa League play-off spot instead of taking a step closer to joining Europe’s elite in the Champions League group stages.
MALMO FF: Melicharek, Andersson, Ricardinho, Jansson, Mutavdzic (Rexhepi 46), Figueiredo, Hamad, Pekalski, Durmaz, Larsson, (Stenstrom 33), Mehmeti (Aubynn 68).
RANGERS: McGregor, Papac, Bougherra, Juanma Ortiz (Hemmings 84), Wallace, Whittaker, McCulloch, Edu, Davis, Jelavic, Naismith.
Ref: Vladislav Bezborodov (Russia).