Mitchell rescued the Rapids from 93-6 in pursuit of 255 in 48 overs as he reached his 100 off 117 balls with six fours.
He received sterling support from Ed Barnard in a stand of 58 and then skipper Joe Leach in an unbroken partnership of 104 in 17 overs.
Two runs were required from the final delivery but Joe Mennie delivered a wide and Mitchell and Leach scrambled the extra run to take the Rapids over the line.
The three-wicket win was their third in four matches and dealt a big blow to Lancashire’s hopes of reaching the knockout stages.
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England all-rounder Moeen has spent the last six weeks playing in the Indian Premier League and lost his Test place for the opening game of the current series against Pakistan at Lord’s.
The 30-year-old had a modest return of one wicket for 49 runs from nine overs as Lancashire totalled 254-9 and then struck a quickfire 24.
Australian paceman Mennie’s three-wicket burst – including Moeen – put Lancashire in the driving seat but then came Mitchell’s rescue act.
Lancashire were put into bat and Josh Tongue picked up a wicket with his first legitimate delivery as Keaton Jennings (5) nicked to first slip.
Alex Davies (27) went for an aggressive swing over midwicket and was caught behind off Charlie Morris but then Karl Brown and Liam Livingstone laid the foundations for the innings with a stand of 76 in 13 overs.
Livingstone lofted Barnard over mid-wicket for a towering six before the former England Under-19 player made a double breakthrough, Brown (48) and Dane Vilas (2) both bowled after expansive drives.
Livingstone went to his half-century off 48 balls with a six and three fours but, after making 67, he fell victim to a brilliant full-length catch by keeper Ben Cox off Tongue.
After a brief delay for safety reasons because of nearby lightning, the visitors’ innings lost momentum as Jordan Clark was LBW to Leach and Brett D’Oliveira had Josh Bohannon and Mennie also leg before.
Moeen had Steven Croft (28) caught behind but Graham Onions (30 not out) and Matthew Parkinson added an unbroken 38 for the final wicket.
Onions then quickly made an impact with the ball as Worcestershire lost opener Joe Clarke leg before in his first over, but it was Mennie who made decisive inroads.
His South Australian team-mate Travis Head was bowled for 17 after aiming a big hit over mid-wicket, and after Moeen pulled a couple of boundaries, he tried to repeat the same shot on 24 and holed out.
Mennie then collected a third scalp as D’Oliveira picked out Davies on the mid-wicket boundary.
Jennings also got in on the act as Cox departed to a stunning catch by Croft and Ross Whiteley edged to Vilas.
Mitchell and Barnard joined forces to launch the recovery, and though Barnard (28) was eventually LBW to Parkinson, Leach (42 not out) also proved a valuable ally.