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.
Falcao stroked in a third from the penalty spot in the 59th minute and was given a rousing ovation when he was replaced by Tiago 10 minutes from time.
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," said Falcao, clutching a match ball for signing by his team-mates.
"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.
Coach Marcelo Bielsa again left Spain pair Javi Martinez and Fernando Llorente out of his squad as they attempt to seal their exits before the transfer window closes on Friday.
Bundesliga side Bayern Munich are trying to complete a deal for versatile defensive midfielder Martinez, while towering striker Llorente has been linked with a move to Italian champions Juventus.
Promoted Valladolid maintained their impressive start to the campaign on Monday when Victor Perez netted twice from the penalty spot in a 2-0 home win over 10-man Levante.
The Castilians were ahead in the 38th minute at their Jose Zorrilla stadium after Levante defender David Navarro handled the ball in the area and was shown a second yellow card.
Perez stroked the ball past Gustavo Munua and added a second from the spot three minutes after the break when Papakouly Diop felled Omar.
Valladolid coach Miroslav Djukic, a former Serbia manager who played for Deportivo Coruna and Valencia, warned his players not to let their early success go to their heads and to focus on securing their top-flight status for another season.
"We know what our goal is and right now it's 39 points away," Djukic said.
"I am very pleased but we still have a lot of room for improvement," he added.