Falcao, who was the centre of more transfer speculation this week with Manchester United mooted as a possible destination this summer, struck in the 27th and 47th minutes to take his tally to 30 in all competitions this season.
Diego Costa, Raul Garcia and Filipe Luis were also on the scoresheet as Diego Simeone's men made it 14 wins from 16 league matches at the Vicente Calderon this season while also keeping up the pressure on second-placed Real Madrid.
Atletico, who have not finished in the top two since winning the league and cup double back in 1996, were three points behind their bitter rivals coming into this weekend's fixtures after drawing their last two matches.
There was rarely any doubt they would not get back to winning ways on Sunday , though, with Costa setting them on their way as early as the fourth minute.
The Brazilian got on the end of Cristian Rodriguez's cross to send a glancing header past Roberto Fernandez and open the scoring.
Atletico continued to press and were rewarded with a second goal just before the half-hour mark when Falcao slid the ball home from close range after being set up by Garcia.
Carlos Aranda missed a chance to get Granada back into the game when he headed wide and Atletico ensured their relegation-threatened visitors would not get the opportunity to cause an upset when they made it 3-0 immediately after half-time through Falcao's second of the match.
Rampant Atletico came close to making it 4-0 in the 57th minute but Garcia was denied by a brilliant save from Roberto before the midfielder struck the post with his follow-up.
Garcia did not have to wait much longer to get his goal though as he got on the end of Koke's 61st-minute free-kick to fire into the roof of the net at the near post.
Falcao spurned a decent chance to notch his hat-trick before Atletico completed the scoring in the 70th minute through Filipe Luis.
Granada felt the Brazilian was offside when he latched onto Adrian Lopez's pass inside the area but there was no whistle and the full-back's dinked cross-shot was deflected in off Roberto's hand.