The League One leaders earned themselves a third round tie against Premiership Charlton courtesy of goals from Nathan Tyson and Nicky Southall.
But the Conference South side gave Colin Calderwood's title favourites a real scare in front of the television cameras.
Salisbury squandered a host of chances to score with their first effort on target not coming until the 91st minute when Luke Prince saw Paul Smith make his only save of the match.
They will complain that Southall's decisive strike in the 81st minute was clearly offside.
But by that stage they had had plenty of opportunities to drag themselves back into the match following Tyson's 53rd minute opener.
In the first two minutes Sammy Clingan came close for Forest with a driven effort that flew narrowly wide of the post from 30 yards, while Grant Holt also spurned two decent opportunities by twice heading high of the target.
But after an initial flurry of pressure from the home side it was Salisbury who grew in strength and carved out several decent opportunities to score.
Simon Browne planted a firm header just wide of the post from an Aaron Cook free-kick and Matt Tubbs just failed to make contact with a fine cross from Matthew Holmes when the slightest of touches might have been enough to steer it home.
Kris Commons came close for the home side as he tormented the Salisbury defence with a twisting run that saw him ride three challenges on his way into the penalty area.
Tyson and Junior Agogo both only missed the target by a matter of inches after finding room in the box and Tyson forced another save from Ryan Clarke with another powerful strike as Forest looked for a the opening goal.
If Forest were to take the advantage it always seemed likely that it would be through the duo and so it proved as they combined seven minutes into the second half.
Gary Holt fed a neat ball into the path of Agogo who played an even better pass to send Tyson through on goal. Keeper Clarke was a little unlucky as he got a hand to the striker's low shot but not enough to prevent it rolling over the line.
Salisbury missed further opportunities to score and were made to pay the price as Forest did make it 2-0, albeit in controversial circumstances.
Tyson appeared to be in a clear offside position as he raced clear of the defence but was allowed to continue and square the ball into the path of substitute Southall who provided a simple finish beyond the exposed Clarke.
That ended Salisbury's fight and earned Forest a New Year date against Charlton.