Academica stunned the Alvalade when Leandro Silva rolled the ball into the Sporting area from a corner and Rafa Soares, left completely unmarked, scored with a first-time shot in the eighth minute.
Adrien levelled for the hosts when he cut inside his marker to fire past Pedro Trigueira, then Carlos Mane wriggled past two defenders on the right to set up Bryan Ruiz for Sporting's second in the 43rd minute.
In between, Jesus, who has a reputation for volatile behaviour, was sent off after remonstrating angrily with the fourth official on the touchline.
Academica levelled with an own goal by Ewerten just before the hour but then had Aderlen sent off with 10 minutes left.
Montero fired the winner with a shot between Trigueira's legs in the 84th minute when he was left unmarked on the left of the Academica area.
The win kept Sporting are five points clear of Porto, who won 3-1 at Estoril, and Benfica, who visit Moreirense on Sunday.
Diego Carlos gave Estoril an early lead before Vincent Aboubakar and Danilo Pereira replied to put Porto 2-1 ahead at halftime and Andre Andre sealed the points with eight minutes left.
(Writing by Brian Homewood in Berne; Editing by John O'Brien)
