Rodriguez entered the match shortly after his team missed a penalty kick early in the second half, scoring the equalizer with a shot from close range in the 74th minute.
The result extended Getafe's unbeaten streak at home to seven matches in all competitions.
Inaki Williams put the visitors ahead in the 13th minute at Coliseum Alfonso Perez. Jorge Molina evened the match by converting a penalty kick in the 21st and Raul Garcia put Athletic ahead again three minutes into the second half.
Molina had a penalty stopped by Athletic goalkeeper Iago Herrerin in the 51st.
Getafe moved to seventh in the standings with 27 points from 20 matches.
Athletic, unbeaten in eight matches in all competitions, is in 10th place with 26 points.
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