Rodriguez saw red in the 55th minute for his second bookable offence, and Atletico scored twice in the next 10 minutes through Gabi and Diego Costa as rock-bottom Real Betis were made to pay.
It was a sudden capitulation from Betis, who had frustratedAtletico for long periods in the first half. The Sevilla club, knocked out of the Europa League by rivals Sevilla on Thursday night, have turned their focus completely to trying to dig their way out of a significant hole at the foot of the standings but are running out of time.
A sudden rush of chances as soon as the game kicked off was hardly a sign of things to come.
Juanfran and Juan Carlos had early sighters for Betis while Diego Costa twice missed the target for Atletico inside the opening 10 minutes, but - aside from Mario Suarez's long-range effort which drifted over the crossbar in the 25th minute - they proved the only efforts on goal of the entire first half.
There was a quick start to the second half too as Juan Carlos struck the post in the 48th minute, but things turned after Rodriguez - booked for a first-half foul on Diego Godin - handled the ball and received his marching orders.
Barely three minutes later, Gabi drilled the ball home from 30 yards and Betis' game plan was in tatters.
Raul Garcia fired narrowly wide from close range moments later but Atletico did not need to wait long for a second, with Diego Costa nodding in Koke's cross in the 64th minute.
Betis did not have the wherewithal to mount a comeback, barely mustering a chance in response.
Jose None's long-range effort sailed wide in the 78th minute, but Atletico saw out another win with ease.