Dercksen continued her good form in the tournament, striking a career-best 81 from 80 balls while Tryon smashed 67 off 43 deliveries but the Proteas could only reach 314-7 chasing a target of 338.
There was good support from the middle-order with debutant Miane Smit, batting at number 3, scoring 39 while Nondumiso Shangase (36) and wicketkeeper Sinalo Jafta (21) made solid contributions.
Nadine de Klerk (22 not out from 13 balls), together with Tryon, kept the fight going until the final over but the Proteas ultimately fell short and were condemned to a third consecutive defeat in the tournament.
India's mammoth total was built around a century by number 5 Jemimah Rodrigues, who scored a career-best 123 off 101 balls, while Deepti Sharma blazed her way to 93 from 84 deliveries.
The Proteas bowling unit struggled in the sapping heat in Colombo and they could not restrict a rampant India outfit, with opener Smriti Mandhana laying the platform with 51.
Masabata Klaas and De Klerk took two wickets apiece while spinner Nonkululeko Mlaba also had two scalps but was expensive going for 71 in her eight overs.
The Proteas still have one match remaining in the tournament, against host nation Sri Lanka, and even though the game will be a dead-rubber in the context of the series will still want to leave on a high.
India top-order batter Ishan Kishan has been ruled out of the second T20I in New Zealand due to a groin strain, with teenage star Vaibhav Sooryavanshi poised to return to the starting XI.
India earned their highest-ever T20I run chase when they successfully chalked off New Zealand's 225/4 with four wickets remaining in a run-soaked encounter in Christchurch on Thursday night.
Less than eight overs were bowled in the fifth and final T20I between India and West Indies as heavy rain fell in Bengaluru.
India star seamer Jasprit Bumrah is doubtful to feature during the upcoming five-match ODI series against New Zealand in November despite being fully fit.
