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The Colombia striker known as the tiger took his tally against the Basque club to seven in three matches following last season's doubles in the 3-0 Europa League final victory and a 2-1 success in La Liga.
His first on a warm night at a vibrant Calderon came in the 18th minute when he left marker Mikel San Jose for dead and dinked the ball over onrushing Bilbao goalkeeper Gorka Iraizoz from a narrow angle.
Three minutes before the break he leaped acrobatically to volley home a Diego Godin centre at the far post, a goal reminiscent of Johan Cruyff's famous effort for Barcelona against Atletico in the early 1970s.
Article continues belowThe Portugese midfielder was only on the pitch for three minutes before he lashed a superb drive high into the net from 20 metres for Atletico's fourth.
"Everyone on the team played at a great level and obviously that paves the way for individuals to shine," Falcao, clutching a match ball for signing by his team-mates, said in an interview with Spanish television.
"The important thing is to gel as a team and start to collect victories and if I can help by scoring a lot more goals than last season so much the better," added the 26-year-old, who netted 24 in La Liga in 2011/12 and 12 in the Europa League.
Atletico's impressive victory after last weekend's 1-1 draw at Levante put them on four points, two behind Barcelona, Real Valladolid and Rayo Vallecano, the only teams to win their opening two matches.
It was a wretched night for Bilbao in the Spanish capital and they have now conceded nine goals after last weekend's 5-3 home thrashing by Real Betis.
They looked a shadow of the side that blazed a trail in Europe last season and reached the King's Cup final, barely troubling Thibaut Courtois in the Atletico goal.
