Arouca coach Vidigal and Sporting defender Naldo were both sent off following the incident in the 88th minute.
Vidigal went on to the pitch and pushed Naldo following a foul near the touchline, then Naldo retaliated on the former Angola coach who went tumbling over although he appeared to make the most of the incident.
Almost immediately, Islam Slimani scrambled home a 90th minute winner with his ninth league goal of the season to give unbeaten Sporting a 1-0 win which kept them five points clear of Porto at the top.
Porto, who have yet to concede a goal in six league outings at the Dragao stadium, overcame Vitoria Setubal 2-0, although they had to wait until the 70th minute for the breakthrough.
Vincent Aboubakar headed Porto into the lead and Miguel Layun scored with a shot on the turn from the edge of the area to secure the points.
"We took a long time to score," said Porto coach Julen Lopetegui. "We created lots of chances and the team show we have a strong mentality."
Titleholders Benfica went third with a 2-0 win at home to Boavista after Goncalo Guedes and Mehdi Carcela scored late in each half.
(Writing by Brian Homewood in Berne, editing by Pritha Sarkar)
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