The Oxford Street side were crowned champions after victory over Wigton last week and showed no let up against the Poolsiders.
The visitors batted first and were all out for 157, with professional Syed Shahabuddin top-scoring with 63 and Robert Bell compiling an innings of 50.
In reply, Furness reached their target with six wickets to spare, Brad Chapples hitting 59 and Nathan Waterston 50.
Workington defeated Whitehaven in a low-scoring affair, dismissing the visitors for 112 – Andrew Ireland taking 5 for 9 – and knocking the target off for the loss of six wickets.
Cockermouth were winners at Cleator, while there was no play between Keswick and Cleator due to rain.
Dalton have been crowned Division One champions – and completed the league and Sowerby Cup double – after victory over Seascale.
The West Cumbrians were all out for 102, with Mike Walker returning figures of 5 for 4, and Dalton had no trouble knocking the runs off for the loss of just three wickets.
Lindal Moor were victorious by 55 runs at Carlisle, Millom defeated Egremont and Workington A overcame Ulverston by 28 runs.
Kirkby are five points clear at the top in Division Three after a six-wicket win at Lindal Moor A.
The home side could only reach 99 batting first, thanks in large part to Mike Etchells taking 6 for 18.
The Villagers knocked the runs off for the loss of four wickets.
They face second-placed Vickerstown at the Community Centre this weekend in a match which will decide the destiny of the title.
Hawcoat Park defeated Furness A by five wickets in their match, reaching their target of 105.
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