They picked up a ninth win from 12 matches to date, though they had to work hard before winning by two wickets at Fulwood and Broughton.
In a match reduced to 46 overs per side at Highfield, the home side batted first and posted 175-9.
Matthew Smith (36) and Lewis Wellings (26) made good contributions but wickets fell regularly as Fulwood and Broughton slipped to 99-6.
However, Abhay Negi (58) and James Lupton (20 not out) aided their recovery, despite excellent bowling from Jamie Thomson.
He took 6-52 from 14 overs with Matt Grindley (2-44) and Matthew Siddall (1-45) also picking up wickets for Blackpool
Despite losing Ben Howarth (14) in reply, Paul Danson’s men looked well set when they made it to 91-1.
That was when Sam Dutton fell for 47, heralding a spell which saw seven wickets fall for 56 runs.
Negi (3-35) and Chris Brookes (3-51) were the men responsible, the latter dismissing Ciaran Johnson (44) as well as Shivam Chauhan and Josh Boyne, both without scoring.
With Blackpool 147-8 and the game in the balance, Grindley (17 not out) and Thomson (16 not out) added an unbroken 31 to see them home with four balls left.
There were differing fortunes at the other end of the table, however, for St Annes and Fleetwood.
St Annes collected a third win of the season in beating Morecambe by 118 runs at Vernon Road.
Batting first, St Annes saw Tom Higson (74) and Luke Jardine (56) put on 147 for the first wicket.
Nathan Bolus and Nathan Bend both contributed 33 as St Annes’ innings ended with them on 238-5.
That was far too stiff a target for Morecambe to chase as they were all out for 120 with 15 overs remaining.
Harry Birkman and Mitch Bolus quickly reduced them to 24-3 as the St Annes attack enjoyed repeated success.
Morecambe captain Ryan Pearson offered the main resistance with 67 but, once he was the ninth man out on 117, the end arrived quickly.
Birkman finished with 4-28, Higson 2-19, Curtis Fletcher 2-33, Thomas Bradley 1-15 and Mitch Bolus 1-24.
It was a day to forget for Fleetwood as they lost by 165 runs at Longridge.
Josh Mullin (52) and Zac Christie (50) both made half-centuries as the home team batted first and made 210 all out.
Dyllan Matthews led the Fleetwood bowling with 4-57, backed up by Declan Clerkin (2-42), Jack Wilkinson (1-23) and Jeremy Davies (1-27).
Fleetwood’s reply ended inside 13 overs though as they were bundled out for 45.
Matthews (17) was the only man making it into double figures in an innings where five men were out without scoring.
Jon Millward took 4-22 for Longridge but the honours were taken by his team-mate Will Vause, who took a hat-trick in his 6-18.
In the Liverpool Competition, Lytham’s hopes of back-to-back wins were ended with defeat at Birkenhead Park.
After snapping a five-game losing run against Northop Hall a week earlier, Matt Taaffe’s players lost by 40 runs in a low-scoring match.
Both sets of bowlers dominated with Lytham dismissing their hosts for 99.
Zia Ur Rehman Akbar was again among the wickets, picking up 5-30 which included the dismissal of Birkenhead Park’s top scorer Michael Barnes (31).
Tom Hessey (2-10), Tom Myerscough (2-28) and Peter Burn (1-22) collected the other wickets for a Lytham side whose reply saw them shot out for 59.
The damage was done by Birkenhead Park opening bowler Satyajeet Bachhav, who claimed 6-19 from 13 overs.
He took three early wickets as Lytham slumped to 12-4 with Richard Staines (14) top scoring before he was the last man out.
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