Colin Calderwood's side had failed to win in four matches and their place at the top of the table looked at risk after Rory Fallon's first-half strike had put Swansea into a deserved lead.
But Forest responded with a much improved second-half display as the visitors were swept aside thanks to two goals in two minutes from James Perch and Kris Commons and a decisive third goal in the 67th minute from Junior Agogo.
It had been all Swansea in the first half as the visitors looked like repeating the win they earned at the City Ground last season.
Forest had an early opportunity after a clever dummy by Agogo let the ball run through to Commons who saw his driven shot charged down.
But from that point on it was Swansea who carved out the better chances.
Andy Robinson was left with his head in his hands after chipping wide of an empty net from 20 yards after a poor clearance from keeper Paul Smith had left him badly exposed.
Izzy Iriekpen headed another effort wide of the post from a corner, while Perch and Ian Breckin had to combine forces with a last-gasp challenge to deny Fallon as he threatened to break clear in the box.
Leon Britton's delivery from the right flank had been a constant threat to Forest and, when the winger forced Wes Morgan to concede the corner, it proved a decisive moment.
Robinson provided pin-point delivery from the right and Fallon pounced with a firm header from six yards to power the visitors into a deserved lead on 42 minutes.
The goal kicked Forest into life and they responded by producing their two best efforts of the half.
Commons' turn on the edge of the box gave him the space to drive a fierce effort which had Andy Oakes at full stretch to palm over in spectacular fashion.
While Agogo's probing run and angled shot inside the box forced a more comfortable but no less vital save from the keeper.
After the break, Robinson forced another adept save from Smith, but it was Forest who clicked into their stride in emphatic fashion with two goals in two minutes
Commons did well to spot Perch's overlapping run down the left and send the full-back racing into the box where he side-footed beyond keeper Oakes.
Then it was Commons' turn to produce the finish after being fed in by John Curtis again down the left-hand channel, although his left-foot strike flew beyond keeper Oakes who had little chance to save.
At this point the whole mood of the match had changed as Forest flowed with confidence and soon made it 3-1.
This time it was Nicky Southall who provided the killer ball for Agogo to race clear and produce a calm, assured finish lofting the ball over the advancing keeper as he charged off his line.
Forest were now completely in charge and substitute Robert Hughes twice came close to making it 4-1, although Swansea held out to keep the scoreline down.