Lancaster had chosen to bat first at Vernon Road, where they were all out for 183 with two balls of their 50 overs remaining.
They lost Eddie Steinson (6) early on before Faizan Khan fell for 32, leaving them 55-2.
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Laurie Atkinson and Irfan Khan doubled the score, putting on 58 for the third wicket.
Khan (29) was the next man out, followed quickly by Jamie Heywood (4) as 113-2 became 118-4.
Atkinson led the Lancaster innings, progressing past his half-century before eventually being dismissed for 65.
That triggered a collapse as Lancaster lost their final six wickets for only 34 runs.
The dismissal of Steven Fisher (6) saw them 151-6 before Yohan De Silva ran through the lower order.
Having earlier dismissed Atkinson and Heywood, he sent back David Steinson (1), Kieran Moffat (5) and Liam Moffat (12) to finish with 5-42.
Lee Sparks (9) was the last man to fall, leaving Lancaster with a decent score to defend.
They did so in style, skittling the home team for 93 inside 21 overs as Liam Moffat and Ben Simm bowled unchanged throughout.
Liam Moffat sent back Tom Higson (0) before Simm dismissed Alex Bradley (4) and De Silva (4) to leave the score 13-3.
St Annes rallied, reaching 45-3, only to lose another three wickets for only two runs.
First to go was Lukman Vahaluwala, who had struck 27 from only 18 balls before he was run out.
Simm accounted for Nathan Bolus (6) and Liam Moffat then dismissed Andy Drake (0) first ball.
The same bowler then got the better of James Bradley (0) and Nathan Bend (23) as St Annes collapsed to 72-8.
Mitch Bolus and Harry Birkman added 21 before the former was out to Liam Moffat for four.
With Luke Jardine unable to bat, that ended the St Annes innings with Birkman finishing 17 not out.
Liam Moffat took 5-26 and Simm 3-59 for a Lancaster team who sit eighth in the table going into Saturday’s home match against Netherfield (12.30pm).