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.
The 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.
