The former New Zealand opener, who quit international cricket three years ago after only modest success, was in commanding form with his hundred coming in just 84 balls as One-day specialists Gloucestershire booked their seventh Lord's final appearance in six years.
Gloucestershire will now face Worcestershire in the showpiece match on August 28 in a repeat of last year's final.
Yorkshire, after winning the toss, made a by no means indefensible 243 for six from their full 50 overs.
But 32-year-old right-hander Spearman made a nonsense of that target in a 122-ball innings featuring four sixes and 14 fours.
England-qualified Spearman, brought to Gloucestershire by John Bracewell - now New Zealand coach - was in dominating form right from the start.
He hit teenage Yorkshire quick Tim Bresnan out of the attack after just two overs and even experienced all-rounder Ian Harvey, Spearman's former Gloucestershire teammate suffered.
Spearman picked up Bresnan for successive sixes over mid-wicket and square-leg and then clipped England pace bowler Matthew Hoggard for six over a longer square boundary. He twice struck Bresnan's replacement Harvey past cover.
Earlier it needed an unbeaten 80 from Australia's Darren Lehmann to get Yorkshire to a decent total after three batsmen, including England skipper Michael Vaughan, gave their wickets away in the 30s.
Harvey, fresh from a stunning Twenty20 hundred against Lancashire, batted curiously low down at number six.
He looked as if he was about to take the visitors to a bigger score with a dashing 20 from just 10 balls when he sliced a wide full toss from New Zealand left-arm quick James Franklin to Michael Hussey at backward point.
Yorkshire's innings had been hampered by a 45-minute rain-break and overcast conditions while Gloucestershire's reply took place in bright sunshine.
But that could not excuse some slipshod bowling and sloppy fielding while Yorkshire skipper Matthew Wood did not help his cause with over-defensive fields and a lack of bowling changes.
However, whatever Wood had tried in the field the chances are that Spearman - who in June broke England legend WG Grace's 128-year-old record first-class score for the County with 341 against Middlesex - would have been equal to it.
Early on Franklin, signed after being called up into New Zealand's England tour squad after playing in the Lancashire League, was expensive with his 10 overs costing 60 runs in total.
But Yorkshire-born left-armer Mike Smith (one for 29 from 10 overs) and off-spinner Martyn Ball (one for 31 off 10) were miserly and showed the value of taking the pace off the ball, something Yorkshire's bowlers were unable to do.
In the other semi-final, England One-day outcast Vikram Solanki's 127 steered Worcestershire to a 41-run win against local rivals Warwickshire at Edgbaston.
Now Ben Smith's men have the chance to make amends for last year's one-sided seven-wicket defeat by Gloucestershire at Lord's.