The Tykes remain bottom and without a win since the opening weekend of the season having failed to earn new boss Gerhard Struber his first point since taking over.
Middlesbrough emerged with a victory for only the third time in 19 matches under head coach Jonathan Woodgate after Fletcher's winner nine minutes after half-time.
The former Barnsley loan star, who scored in the 2-2 draw with Hull on Sunday, hit his fourth goal of the season to lift Middlesbrough out of the relegation zone.
It was a game between the two Sky Bet Championship teams with the longest winless runs in the division and played on a cold and wet night on Teesside.
Middlesbrough needed a break but are short of experienced options, young goalkeeper Aynsley Pears and left-back Hayden Coulson were replacements for the injured Darren Randolph and suspended Marvin Johnson.
The wet conditions, with water splashing every time a player kicked the ball, did not help either team and it inflicted a blow to Middlesbrough's Anfernee Dijksteel inside 23 minutes when he jarred his knee after slipping, which forced him off.
By that time, there was an early chance at both ends. Pears let Dimitri Cavare's cross slip from his grasp after the full-back got to the byline and both Lewis Wing and Jonny Howson had to block efforts from Luke Thomas.
At the other end, Britt Assombalonga looked to have scored. He darted beyond Bambo Diaby and his shot over goalkeeper Samuel Radlinger had to be hooked clear by Ben Williams on the line.
That was as close as either side got before the break, and the sight of Assombalonga limping down the tunnel was not what Middlesbrough's frustrated fans wanted to see at the half-time whistle.
The £15million man did return to the field and he was to play a crucial part, but Middlesbrough were on the back foot straightaway. Within four minutes, Jacob Brown curled an effort against the crossbar as Barnsley made the home crowd more nervous.
But Assombalonga was involved in the opener. His pass down the line had no right to end where it did but Cavare allowed Marcus Tavernier to the ball first.
Tavernier rolled it onto Fletcher, whose first touch led to Radlinger and Mads Andersen slipping, and the former Barnsley man had the simple task of tapping into the empty net.
After that Barnsley pushed briefly without testing Pears and then Radlinger had to make a number of saves to deny Coulson and Assombalonga twice as Middlesbrough finally clinched maximum points for the first time since September 14.