Cornish Pirates produced an inspired second-half display to reach the Championship play-off final.
London Welsh enjoyed the better of the first-half, Matt Corker's try proving just reward for their dominance.
But the second-half saw the Pirates slowly gain the ascendancy, captain Gavin Cattle proving the catalyst.
The veteran scrum-half grabbed his side's first try, before making the break that put in wing Rhodri McAtee for the score that made the game safe.
The Cornish club now face a two-leg play-off final against Worcester Warriors, who had earlier beaten Bedford 23-22.
The Pirates will have home advantage for the first leg at the Mennaye Field on Wednesday 11 May (1945 BST).
They then go to Sixways for the second leg the following Wednesday night (18 May, 1945 BST).
And the Pirates have the psychological bonus of knowing that they are the only side to have beaten Worcester in the Championship this season, after Rob Cook's late penalty earned a 23-21 win at Sixways back in October.
The Pirates' progression into the final initially looked in doubt on a sodden Penzance afternoon as Welsh were quickest out of the blocks, centre Simon Whatling making much of the early running with several incisive breaks.
The visitors' reward came in the 16th minute when, after several phases of attacking play, Corker found the necessary space to squeeze over for the game's opening try.
As the half progressed the Pirates began to enjoy a greater share of possession, stringing together several phases of attack to test the Exiles defence.
The Cornish outfit thought they had their reward when Harlequins-bound centre Matt Hopper made a superb break, only to be held up short.
But, with both sides having kicked first-half penalties, Welsh went in at half-time with a 10-3 advantage.
The second-half saw Chris Stirling's men employ a change in tactics, utilising the favourable wind and the boot of fly-half Johnny Bentley to put themselves deep into Welsh territory.
As the game entered its final quarter the home side seemed to find another gear, ramping up the pressure on their already strained opponents.
On 64 minutes Cattle took advantage of a rare lapse in the Welsh defence to sneak over on the blindside following a breakdown five metres out.
Cook's conversion brought the scores level and, when he slotted over a second penalty to make it 13-10 moments later, the tension amongst the Penzance crowd visibly lifted.
A ground that had been full of nerves was quickly restored to a vibrant throng as Cattle unlocked the Welsh defence once again, this time releasing McAtee who made no mistake as he went over.
Although Cook missed the conversion, it was of little significance as the full-time whistle blew shortly afterwards, confirming the Pirates' place in the final.
Cornish Pirates head coach Chris Stirling:
"I'm absolutely rapt for the boys that all of their hard work paid off.
"We were pushed to the limit by London Welsh and full credit to the boys for coming through.
"I don't think we kicked overly well but Welsh were tiring as the game went on and, when we shifted it wide, we did well."
Cornish Pirates: Cook; McAtee, Hopper, Luke, Jackson; Bentley, Cattle; Andrew, Ward, Paver, Myerscough, Gulliver, Morgan, Betty, McGolone.
Replacements: Rimmer, Elloway, Burgess, Marriott, Doherty, Winn, Locke.
London Welsh: A Thomas; Gibson, Tonga'uiha, Whatling, Claassens; Ross, R Lewis; Pittman, Ma'asi, Ward, Powell, Corker, Mills, Hills, Russell.
Replacements: Lahiff, Purdy, Beach, Stevenson, Shabbo, Yarde.