Falcao scored in the 32nd minute to cancel out Raheem Sterling's opener, but he couldn't convert from the penalty spot early in the second half. The two sides would trade plenty more goals, with Man City eventually winning 5-3 in the first leg of the round-of-16 encounter.
After Kylian Mbappe helped Monaco regain the lead in the 40th minute, Sergio Aguero countered with a goal of his own in the 58th to tie the game for City. It was the first of two goals for Aguero on the memorable Champions League night.
Falcao managed to make up for an embarrassing missed spot kick to give his side a one-goal edge with a beautiful chip shot over goalkeeper Willy Caballero, and for a moment it appeared the former Manchester United flop would be the hero for the Ligue 1 side.
But Man City went on to once again even the game thanks again to Aguero, and then John Stones gave City a 4-3 lead in the 77th minute.
Leroy Sane put the icing on the cake in the 82nd minute to give his team a 5-3 victory in the thriller.