Off-spinner Graeme Swann struck twice in the space of 21 runs to leave Sri Lanka on the back foot in the second and final Test against England in Colombo on Friday.
England, beaten by 75 runs in the first Test in Galle, need a win to level the two-match series and retain their world number one Test ranking.
Dilshan was unfortunate to depart, caught in the slips off Swann, as TV replays proved inconclusive whether the ball had gone off the bat.
Dilshan, who earlier in the day had been fined 10 percent of his match fee for excessive appealing in England's first innings, walked off clearly unhappy with the decision.
The infra-red Hot Spot technology, which could have determined an edge, is not being used for the series.
Dilshan, who made 35, has now gone 21 innings without a Test century since making 193 against England at Lord's in June last year.
Later in the same over, Swann appealed for leg-before against Sangakkara, which Oxenford turned down. This time it was England's turn to lose the review even though the ball clipped the off-bail.
But Sangakkara did not last long as he edged Swann to wicket-keeper Matt Prior after making 21, with Sri Lanka still 61 runs in arrears.
The left-hander, who had been dismissed first ball in two of the three previous innings, finished the series with a dismal average of 8.75.
Left-handed Thirimanne failed to take advantage of a missed stumping off Swann and edged Anderson to Andrew Strauss at first slip after making 11.
Prasad, a tailender who averaged 19.20 in his previous nine Tests, defied the England attack for 87 minutes and even helped himself to five boundaries.
Prasad was dropped twice in one Swann over, as Prior failed to glove a thick edge and Finn floored a waist-high catch at mid-off.
Source: AFP Global Edition