Cheadle's Chris Barker loses his wicket to a ball from Matt Goodwin, top left. Pictures by Malcolm Hart
The Blythe captain played his part with figures of 4-47 to help dismiss Cheadle for 122.
Matt Goodwin also impressed with a late cameo to take the final four wickets.
Gary Wilson (34), Haydon Simcock (26) and substitute pro Farhaan Behardien (20) then added key runs with the bat to ensure Blythe claimed local bragging rights.
Finch said: "Winning the toss was a big factor.
"The wicket did get easier to bat on, but we bowled well.
"I got four wickets and the pro got two. Goodwin then grabbed four in six overs.
"In reply, we were 83-2 before the substitute pro was run out. He was batting fantastically well – if that hadn't happened I think we'd have got there with the loss of just two wickets."
Blythe were once again forced to call upon a different substitute pro in their bid for a third successive victory.
Imranullah Aslam inspired the previous week's eight-wicket victory over Rode Park & Lawton.
And on Saturday, Blythe again came up trumps with the acquisition of South African all-rounder Behardien.
The fast bowler accounted for both Cheadle openers.
Jake Thompson was bowled for a duck while Darren Plant sent a catch to Gary Wilson on 23 after threatening to run up a big score.
But it was Finch who claimed the prize wicket of third batsman Dave Wheeldon after Cheadle's pro presented a catch to Goodwin.
When 31-3 became 38-5 Cheadle were in trouble. Matthew Coxon attempted to spearhead a recovery, but lost partner Shaun Rashid (15) after the 21-run partnership looked to be gathering momentum.
Another 23 runs were added before Chris Barker became Goodwin's first victim and his departure sparked a second collapse.
Cheadle went from 82-6 to 87-9 and only James Sellers's 29 prevented the side posting an even simpler target.
Blythe openers Gary Wilson and Haydon Simcock then formed an opening partnership of 61.
Wilson (34) was finally dismissed by Chris Barker and the same bowler then took the wicket of Simcock (26).
Blythe then endured what Finch described as their "usual collapse". But despite slipping from 83-1 to 105-6, Dan Hammond (10no) and Simon Owen (5no) held their nerve to see the visitors home.