Inspired by a whirlwind half-century from Chris Gayle on his debut for the county, the Royals reached a victory target of 196 with four wickets and almost six overs to spare - taking them off the foot of the table.
They are now only four points behind Lancashire, who are also facing a battle against the drop after their third one-day defeat this week despite Stuart Law's highest totesport score of the season, and a superb bowling spell by Glen Chapple.
Law made 82 from 86 balls with 10 fours and a six after Lancashire won the toss and chose to bat. But he received little support, with even Andrew Symonds suffering a rare failure, as the Royals' spinners Ray Price and Gareth Batty bowled mean spells.
Price conceded only 32 runs in his nine overs and Batty claimed two for 34, taking a sharp return catch to dismiss Lancashire captain Mark Chilton, then having Law stumped by England Under-19s captain Steven Davies at the second attempt.
That left Lightning on 133 for five but Chapple and Kyle Hogg seemed to have put them back on course with a sixth wicket stand of 44 inside eight overs.
Chapple was then run out for 29 by Worcestershire's captain Vikram Solanki, the first of four wickets to tumble for nine runs - two of them to Gayle.
The West Indies all-rounder then smashed 53 from 40 balls to give the Royals' reply a flying start. Chapple hit back for Lancashire by bowling Gayle, then having Stephen Moore and Graeme Hick caught behind in a spell of three for 15 from seven overs.
He ended with four for 23 but Solanki and Ben Smith steadied the Royals' nerves with a fourth-wicket stand of 56, and despite two wickets for James Anderson, Davies steered them home.
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