Marcos Paulo, Salvador Agra and Diogo Valente all found the back of the net as Academica ended a run of four Primeira Liga games without a win.
Academica climb into ninth position in the table as a result, while Arouca remain just three points clear of the relegation zone.
Both sides struggled for fluency, but the visitors adapted the better and struck towards the end of each half to secure victory.
Chances were at a premium in the first period, although Lassad Nouioui spurned an opportunity for Arouca as he ghosted in at the back post but saw the ball skid under his foot before rolling harmlessly out of play.
The Tunisian attacker was made to rue his miss as Academica opened the scoring in the 44th minute, Marcos Paulo cutting in from the right and sending in a low shot that Cassio was unable to get a hand to.
Academica continued to threaten after the interval and went close to doubling their lead when Mame Moussa Gueye struck the post.
The visitors were able to celebrate a second goal with six minutes remaining as Salvador received the ball on the right-hand side of the penalty area and, with no challenge forthcoming, bore down on Cassio before nutmegging the onrushing goalkeeper.
Academica made victory a certainty in the final minute of normal time when Valente got in front of his marker to volley home a cushioned cross.
