Benfica came into the fixture four points clear of local rivals Sporting Lisbon, who sit second, but now hold a seven-point advantage with just three matches left to play.
Rodrigo's fourth goal in his last three matches put the visitors ahead in first-half stoppage time after the Arouca defence failed to clear their lines from a Lima cross.
And Nicolas Gaitan made sure of the points 10 minutes into the second half, as eyes turned towards finishing the job at home to rock-bottom Olhanense on Saturday.
Arouca are not yet assured of safety, sitting two points clear of the relegation play-off position in 13th.
In Sunday's other match, Porto needed goals from Carlos Eduardo and Juan Quintero in the last four minutes to give them a 3-1 win at Sporting Braga.
The result saw Porto bounce back from their UEFA Europa League elimination at Sevilla on Thursday and strengthen their grip on the third and final UEFA Champions League spot.
Silvestre Varela sent the reigning champions into a 23rd-minute lead with a delicate chipped finish, but Erik Moreno pegged them back with a header shortly before the hour-mark.
Brazilian Eduardo restored Porto's advantage four minutes from time though, and Quintero's stoppage-time effort sealed the points.
Victory lifts Porto nine points clear of the fourth-placed Estoril, who face Pacos de Ferreira tomorrow, while Braga's hopes of European football next season are fading.
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