A torrential downpour then kept the players off the pitch and prompted the match officials to finally abandon the day's play.
England, who are 3-1 down in the series, will return to chase down their target in 50 overs.
For inspiration, the tourists can look back on the 2004 Champions Trophy match at Southampton against the same opponents. That spilled into the reserve day, before England captain Michael Vaughan and his men won it under the Duckworth-Lewis method.
Current skipper Alastair Cook returned to the side after serving a one-match suspension for a second slow over-rate offence in the third ODI and won the toss, putting the hosts in to bat.
He had reason to feel vindicated as the scoreless Kusal Perera edged the third delivery of the match from Steven Finn to second slip.
The other opener, Tillakaratne Dilshan (35), hit six boundaries in his breezy 31-ball knock before dragging a Chris Jordan delivery onto the stumps.
Sri Lanka slumped to 59-3 when Jordan, involved in the first four dismissals, caught Mahela Jayawardene at the lone slip off Woakes.
Sangakkara played with characteristic cool as he and captain Angelo Mathews (40) added 85 runs to steady the innings even though they found boundaries hard to come by.
Jordan dismissed Mathews in the 34th over but Sri Lanka, at 172-4, looked well-placed for a late assault in the final 10 overs.
Woakes, however, had other ideas as the 25-year-old paceman ended Sangakkara's 123-ball stay, claiming five wickets in his last 15 deliveries to hasten Sri Lanka's collapse.
Sangakkara hit 10 boundaries in his fourth successive fifty-plus score.
England's bowlers delivered 15 wides -- with Woakes contributing a third of that total -- in an otherwise disciplined performance.
(Reporting by Amlan Chakraborty in New Delhi; editing by Toby Davis)
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