Rovers slipped to 10th place after being edged out by leaders Newcastle in midweek, but bounced back to exact revenge on their neighbours, who won 1-0 at the Keepmoat Stadium in October, and keep pace with their fellow play-off contenders.
Barnsley were unlucky to finish the game empty-handed after launching a thrilling late rally, but Doncaster held on and have now lost only one of their last eight league matches.
Tykes manager Mark Robins responded to the 5-3 defeat at Bristol City in midweek by recalling Darren Moore, Adam Hammill, Anderson De Silva and Andy Gray, while Coppinger and Jay Thomas-Emmanuel returned for Rovers.
With possible play-off hopes and bragging rights at stake, both sides charged into the fray, but it was Rovers who went close to an early goal when midfielder Mark Wilson's left-footed volley whistled over the crossbar in the fourth minute.
Barnsley responded with Gray heading just wide from Ryan Shotton's long throw-in and Filipe Teixeira forcing visiting goalkeeper Neil Sullivan to catch his 20-yard lob from the right side of the penalty area.
Hammill twice went close midway through the first half, curling a right-footed shot from the edge of the area just wide and then firing straight at Sullivan, who held the winger's stinging drive.
Barnsley's momentum was checked when playmaker Teixeira was forced out of the action in the 29th minute and replaced by Daniel Bogdanovic, who lashed a looping shot over the crossbar from 18 yards soon after.
But Doncaster 35th-minute lead when Emmanuel-Thomas pulled the ball across the edge of the area and Coppinger curled a right-footed shot low into the bottom corner beyond Tykes goalkeeper Luke Steele.
Barnsley almost levelled just before the interval, but De Silva's thumping header from Hammill's corner came back off the crossbar.
Rovers striker Billy Sharp and De Silva traded shots shortly after the restart, Emmanuel-Thomas flashed a 30-yard shot wide and Hammill saw his effort from similar distance well held by Sullivan.
Coppinger was next to try his luck from long range, but Steele was equal to it, while De Silva and Hammill kept Sullivan busy with two more strikes from 25 yards as the home side chased an equaliser.
Visiting goalkeeper Sullivan kept his side in front with a fine save in the 82nd minute, flinging himself full length to keep out Hugo Colace's angled shot from inside the area moments after Coppinger had gone close to doubling Doncaster's lead with a header that flew the wrong side of the post.
Rovers defender Shelton Martis then blocked Hammill's drive and Bogdanovic blazed over the crossbar as Barnsley launched a furious late onslaught in a bid to rescue a point, but Sean O'Driscoll's side held on for the win.