A goal from £1.14million summer signing Joe Garner - his first at the City Ground - was enough to lift Forest off the foot of the table and ease the pressure on the under-fire manager.
Speculation had been rife all week that former Derby manager Billy Davies was lined-up to replace Calderwood.
But his side recorded just their third success of the campaign to earn him a little more time.
The pressure had been on for Calderwood as he waited for the first goal to go in but in the 36th minute he got some relief as Nathan Tyson's pace took him down the left side from where he bent in an inch-perfect cross for Garner to head home from close range.
Prior to that, it had been Barnsley's Jamal Campbell-Ryce who had looked the most likely to score.
He was given the freedom to strike a forceful 25-yard shot that required a smart save from Lee Camp to deny the visitors a third minute lead and seeing a later effort deflected wide of the post.
Jon Macken was left frustrated after spurning a golden chance to put Barnsley ahead, heading wide after Joel Lynch had given away possession to Campbell-Ryce.
Forest responded with a shot that bobbled wide from Robert Earnshaw and a curling effort from Paul Anderson that was deflected off target.
And after Garner had given them the advantage, Forest stepped up a gear again, with Tyson seeing a driven effort of his own drop just wide after taking a deflection in the box.
Inspired by Lewis McGugan, Forest began the second half in spirited fashion, with the midfielder beating three men on a mazy run before squaring the ball to Earnshaw, who was denied by a brave block from Dennis Souza.
While McGugan then lashed a ferocious rising shot against the bar from 20-yards as Calderwood's side went in search of a second.
Camp still had to be alert to make an athletic, stretching save to palm an Anderson Silva strike around the foot of the post.
Heinz Muller had to demonstrate impressive instincts in the Barnsley goal as well as left-back Joel Lynch unleashed a piledriver that the keeper flicked over his bar acrobatically.