every major nation they have played.
The win consolidates Sri Lanka in second position in the Pool A table, although tournament favourites Australia have a game in hand.
England made a brisk start as Ian Bell and Moeen Ali combined for a 62-run partnership in the first 10 overs.
Root looked assured hitting his fourth one-day international century, with Gary Ballance (6) the only real batting failure for England.
The 310 target looked competitive before Sri Lanka, who now have four century makers at the tournament, unleashed their batting prowess.
Openers Thirimanne and Tillakaratne Dilshan made a flying start to the chase, racing to 100 without loss.
Thirimanne was dropped on three and made the most of his life, bringing up his third half-century of the tournament in 58 deliveries.
A change of pace from Ali provided a wicket when Dilshan (44) mis-cued a drive straight to Morgan at mid-wicket.
But it did nothing to stem the flow of runs as Sangakkara came in and blasted a 45-ball half century.
The onslaught continued to the delight of Sri Lanka fans in the New Zealand capital and Thirimanne fittingly ended the match with a booming six off Chris Woakes.
Score Board
England won toss
England
M M Ali c Lakmal b Mathews 15
I R Bell b Lakmal 49
G S Ballance c & b Dilshan 6
J E Root lbw b Herath 121
*E J G Morgan c Dilshan b Perera 27
J W A Taylor c Dilshan b Malinga 25
†J C Buttler not out 39
C R Woakes not out 9
Extras (b 4, lb 3, w 9, nb 2) 18
Total (6 wickets; 50 overs) 309
Did not bat: S C J Broad, S T Finn, J M Anderson
Fall: 1-62, 2-71, 3-101, 4-161, 5-259, 6-265
Bowling: Malinga 10-0-63-1 (2w); Lakmal 7.4-0-71-1 (2nb, 2w); Mathews 10-1-43-1 (1w); Dilshan 8.2-0-35-1; Herath 5.5-0-35-1; Perera 8.1-0-55-1
Sri Lanka
H D R L Thirimanne not out 139
T M Dilshan c Morgan b Ali 44
†K C Sangakkara not out 117
Extras (b 8, lb 1, w 3) 12
Total (1 wicket; 47.2 overs) 312
Did not bat: D P M D Jayawardene, *A D Mathews, F D M Karunaratne, L D Chandimal, N L T C Perera, H M R K B Herath, S L Malinga, R A S Lakmal
Fall: 1-100
Bowling: Anderson 8-0-48-0; Broad 10-1-67-0 (1w); Woakes 9.2-0-72-0 (1w); Finn 8-0-54-0 (1w); Ali 10-0-50-1; Root 2-0-12-0
Result: Sri Lanka won by 9 wickets
Points: Sri Lanka 2, England 0
Man of the Match: K C Sangakkara (Sri Lanka)
Umpires: B N J Oxenford (Australia) and R J Tucker (Australia). TV umpire: C B Gaffaney.
Match referee: D C Boon (Australia)