Keita Balde and Senad Lulic were dismissed in the second half as fourth-placed Lazio, already guaranteed a place in next season's Europa League group stage, threw away an early lead.
Seventh-placed Inter, who had lost six and drawn two of their previous eight league games, had already missed out on European football next season after a campaign which has seen two coaches sacked.
They are now under caretaker Stefano Vecchi.
Lazio went ahead in the 18th minute when Jeisson Murillo tripped Felipe Anderson and Keita fired home the penalty.
Some Inter fans abandoned the Stadio Olimpico in protest midway through the first half and missed their team's three goals.
Defender Marco Andreolli, making only his fifth appearance of the season, headed in from a corner in the 31st minute, then Lazio defender Wesley Hoedt diverted Antonio Candreva's harmless cross past goalkeeper Ivan Vargic six minutes later.
It got worse for Lazio in the second half as Keita was booked twice in quick succession, first for needlessly kicking the ball at Candreva after a foul and then for diving in the penalty area.
Eder scrambled a third goal for Inter before Lulic, previously booked for handball, was dismissed for a late tackle.
(Writing by Brian Homewood in Berne; Editing by Clare Fallon)
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