Coutts headed in substitute Michael Jacobs' corner to earn the Rams a much-needed point themselves as they avoided a third successive defeat.
Chris O'Grady's 47th-minute strike had seemed like lifting Barnsley, thrashed 6-0 at home by Charlton on Saturday, out of the bottom three.
After Derby had enjoyed the majority of the first-half possession and chances, Barnsley broke the deadlock with O'Grady volleying in a cross from impressive debutant Andrai Jones.
But Derby nudged four points clear of the drop zone thanks to Coutts' late leveller to leave Barnsley second from bottom.
Jason Scotland, recalled to the Barnsley starting line-up at the expense of leading scorer Chris Dagnall, had the best two openings of the opening 15 minutes, first lashing a shot high and wide and then failing to test Frank Fielding from 12 yards.
Derby threatened themselves in the 16th minute but Jeff Hendrick, passed fit after suffering a dead leg at the weekend, was denied by a brilliant save from Barnsley keeper Luke Steele.
Steele thwarted Hendrick again in the 23rd minute following the midfielder's turn and shot following Ben Davies' cross and came out on top for a third time after the Irishman unleashed a shot from 25 yards.
The visitors were enjoying a good spell and from a Coutts corner, Jake Buxton planted his 12-yard header wide.
Steele had six put past him as Barnsley crashed to a heavy home defeat to Charlton on Saturday and he was keeping his team in this game as he was again in fine form as the half-hour approached.
He first foiled 16-year-old Mason Bennett, handed his first league start of the season, from the edged of the box before Chris Martin's follow-up effort was superbly blocked by defender Martin Cranie.
But Barnsley made the crucial breakthrough two minutes into the second half, with O'Grady volleying in a Jones cross for his first goal in four games.
The Reds were buoyed by that strike and they came close to doubling their advantage shortly afterwards but Tomasz Cywka's 18-yard effort was well saved by Fielding.
Bennett was replaced by Conor Sammon with 17 minutes left and moments later Martin fired over from 25 yards as the Rams searched for the equaliser, which came at the death via the head of Coutts.