ICC match referee Mike Procter called a disciplinary hearing on Monday after the players' behaviour was reported by umpires David Shepherd and Billy Bowden.
Shepherd was forced to step in after Sangakkara exchanged words with India batsman Mohammad Kaif and later became embroiled in a heated row with Harbhajan Singh.
Procter found the wicketkeeper guilty of a Level 2.9 offence under the International Cricket Council's code of conduct and fined him his entire match fee.
Sangakkara's offence, which could have resulted in a suspension, refers to the use of "language that is obscene, offensive or of a generally insulting nature" to another player, official or spectator.
Chandana and Dilshan were fined 50 per cent of their match fees after being found guilty of a Level 1.4 offence which deals with the more general use of offensive language.
Sri Lanka won the match by 25 runs.
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