The midfielder, who helped shoot down the Reds at the same stage 12 months ago while on loan at Blackpool, was the man sacrificed after just four minutes of a goalless first leg at the City Ground last Thursday following Neil Taylor’s dismissal.
But he proved worth his weight in gold — or at least the estimated £90million (€103m) windfall for the team promoted to the Barclays Premier League on May 30 — in an open and electrifying encounter at a sold-out Liberty Stadium.
David McGoldrick and Fabio Borini had already hit the crossbar at either end before Dobbie’s short corner set up Leon Britton for a stunning 28th-minute opener.
The Scot then added a well-worked second shortly after to give battling Forest a mountain to climb.
Lewis McGugan’s free-kick smacked the woodwork before former Cardiff striker Robert Earnshaw threw them an 80th-minute lifeline.
And after Earnshaw dramatically hit a post in injury time, Darren Pratley sealed victory by finishing from inside his own half after Forest keeper Lee Camp had gone up for a corner.
It is the East Midlands’ side’s fourth failed play-off attempt in nine seasons and a fourth for manager Billy Davies since 2005 having missed out twice with Preston and now with the Reds.
The Swans, 28 years after their only brief spell in England’s top flight, are looking to complete an astonishing six-year rise from the fourth tier and could now face a Wembley showdown with south Wales rivals Cardiff, who face Reading in the other semi-final tonight.
SWANSEA: De Vries, Rangel, Williams, Monk, Tate, Dyer, Dobbie (Pratley 59), Allen (Moore 84), Britton, Sinclair (Serran 88), Borini. NOTTM FOREST: Camp, Gunter, Chambers, Morgan, Moloney, McGugan, Cohen, McGoldrick (Earnshaw 78), Moussi, Tyson (Majewski 62), Tudgay (Boyd 68).
Ref: Andre Marriner (W Midlands).