Dercksen struck 104 off 84 balls while Tryon scored 74 off 51 deliveries as the Proteas amassed a total of 315-9 in their 50 overs after being put in to bat at the toss by home skipper Chamari Athapaththu.
Tryon then returned career-best figures of 5-34, which included a hat-trick, as Sri Lanka were bowled out for 239 in the 43rd over.
The result means the Proteas have only won one of their four matches in Sri Lanka with the host nation set to play India in the tri-series final in Colombo on Sunday.
Opening pair Laura Wolvaardt (33) and Tazmin Brits (38) started positively for the tourists, putting on a partnership of 68 inside 14 overs.
They then however lost their way as a massive collapse saw them lose five wickets for just 17 runs as the Proteas slipped to 85-5 in the 20th over.
It was soon 127-6 but it was at that point that Dercksen, batting at number 7, was joined at the crease by Tryon and the duo combined for a match-defining partnership of 112 off 88 balls.
Dercksen has been the Proteas' player of the tournament on the back of three consecutive half-centuries, all in losing causes, but went one better with a maiden ton for her country that came off 81 deliveries.
The all-rounder was dismissed with just more than six overs to remaining in the innings but that was when Tryon took over the leading role and, together Nadine de Klerk (32 not out off 19 balls), propelled the Proteas above the 300-run mark.
Sri Lanka were made a good fist of the run-chase and were wellplaced at 160-3 after 29 overs but seamer Ayabonga Khaka got the key wicket of home captain Athapaththu for 52.
Tryon then riot with her left-arm spinners as she nabbed a hat-trick in the 42nd over and subsequently completed a five-wicket haul and a player-of-the-match performance.
Annerie Dercksen and Chloe Tryon starred with the bat but it was not enough as the Proteas Women slipped to a 23-run defeat against India in the ODI tri-series in Colombo.
Head coach Mandla Mashimbyi admits the ODI tri-series in Sri Lanka is a "learning curve" for the Proteas Women as they look ahead to the World Cup later this year.
The Proteas Women fell to their second defeat in as many games in the ODI tri-series in Colombo after a five-wicket loss against hosts Sri Lanka on Friday.
Following a tightly contested defeat against India, the Proteas Women remain optimistic and are focusing on the controllables ahead of their second One-Day International (ODI) Tri-Series match against hosts Sri Lanka on Friday.
