The upset left Porto at the top of the league standings, but only one point ahead of Sporting Lisbon and Benfica. Sporting hosts Pacos Ferreira on Sunday while Benfica visits Rio Ave.
Pressure will only increase on Porto's first-year coach, Paulo Fonesca, as his side has managed one win from its last six matches in all competitions.
"We didn't play better than Academica," Fonesca said. "They were more aggressive. We were incapable of breaking through their defense. That's why we lost.
"Clearly, FC Porto is used to winning and we can't be satisfied with the result or our performance."
Academica moved into eighth place with the win.