London Welsh survived a second-leg defeat by Bedford Blues to book a two-legged Championship final against Cornish Pirates.
Welsh, who have applied to join the Premiership should they progress, were 9-7 ahead at the break thanks to three Alex Davies penalties.
However Bedford added scores from Don Barrell and Neil Cochrane to Ollie Dodge's first-half try to take control.
James Pritchard added three conversions and a penalty to seal the win.
Nick Scott got London Welsh's consolation try in the second half.
They will now face Cornish Pirates in the final, with the first leg taking place on 23 May and the second on 30 May.
London Welsh: Davies; Scott, J Lewis, Tonga'uiha, Ajuwa; Jewell, Moates; Moss, George, Tideswell; A Brown, Corker; Mills, Denbee, Jackson.
Replacements: Ma'asi, Pittman, Bateman, G Johnson, Beach, R Lewis, Whatling.
Bedford: Pritchard; Dodge, Burke, Staff, Bassett; Lennard, Baldwin; Reeves, Cochrane, Boulton; Tupai, Howard; Gillanders, Harding, Fisher.
Replacements: Locke, Walsh, Rae, Barrell, Fox, Veenendaal, Vass.