Falcao starred as Club Atlético de Madrid came from behind in impressive style to establish a convincing advantage over S.S. Lazio.
The striker, a UEFA Europa League winner with FC Porto last season, scored in each half after Adrián López had cancelled out Miroslav Klose's 19th-minute opener. It leaves the Serie A side with a mountain to climb in Madrid next week if they are to reach the last 16.
It was an emotional return for Atlético coach Diego Simeone, who was handed a pennant by his former club in recognition of his services as a player, to the acclaim of the home crowd. The Curva Nord were almost silenced within a minute of kick-off, though, when Koke muscled his way past Matuzalem before playing in Falcao to blaze over from a tight angle.
The visitors made all the early running, yet it was Lazio who took the lead when Thibaut Courtois fumbled a routine long shot by Antonio Candreva and Klose reacted first to the rebound. It was hard on Simeone's side but it took them just six minutes to level. Falcao outjumped Giuseppe Biava to head Juanfran's deep right-wing cross into the path of Adrián, who volleyed in from close range.
The Rojiblancos deservedly took the lead on 37 minutes in some style. Adrián's back-heeled flick was controlled in a tight space by Diego, whose centre through a crowded area found Falcao lurking at the far post to fire in.
Lazio tried to up their tempo thereafter, Hernanes ‒ the hosts' brightest light ‒ mistiming both a header and a shot, but they had no answer to the rapid interplay of the 2010 winners, who extended their lead on 63 minutes with a rapier counterattack. Adrián raced down the right before picking out Falcao for his fifth strike of the campaign, and his 22nd UEFA Europa League goal in all.