The Polish midfielder fired home an angled drive in the 64th minute of Saturday's Championship clash at The Valley as Keith Hill's side registered their second win in seven league matches to climb up to 16th place in the table.
It was no less than the Tykes deserved as they dominated from start to finish, while Charlton have now failed to win any of their last five league matches and offered nothing in this encounter until second-half substitute Bradley Pritchard forced visiting goalkeeper Ben Alnwick into a fine save late in the game.
Barnsley were the more enterprising side in the first 20 minutes with midfield trio Stephen Dawson, Jacob Mellis and Tomasz Cywka peppering the Charlton goal with shots from outside the penalty area.
Charlton struggled to mount a threat on the visitors' goal and Barnsley striker Chris Dagnall went close to breaking the deadlock in the 35th minute when his angled effort from inside the penalty area was well held by home goalkeeper Ben Hamer.
Tykes forward Craig Davies, who made his first appearance for Wales in almost five years against Scotland in midweek, was foiled by a Charlton defender Leon Cort's last-gasp block as the visitors continued to chase an opening goal and it was not until three minutes before the break that Barnsley goalkeeper Ben Alnwick was pressed into action.
Barnsley defender Scott Golbourne fouled Charlton midfielder Danny Green on the edge of the area and Alnwick pushed Dale Stephens' subsequent free-kick over the crossbar.
But the Tykes finished the first half on top, with Mellis going close again with a fierce 25-yard effort that whistled wide.
Charlton manager Chris Powell sent on Johnnie Jackson and Bradley Wright-Phillips for Danny Hollands and Abdul Razak respectively during the break in a bid to spark some life into his side.
Barnsley continued to force the play after the restart however and Dagnall went close again in the 53rd minute when he flashed a volley from Mellis' floated free-kick just passed Hamer's right-hand post.
The South Yorkshire side secured the goal they deserved in the 64th minute. The ball was worked neatly to the left side of Charlton's penalty area and Cwyka latched on to the ball and lashed home a venomous right-footed finish high into the roof of the net from 12 yards.
Powell sent on his third substitute, Bradley Pritchard, for Green in the 68th minute, but Alnwick was still redundant in the Barnsley goal as the Addicks struggled to muster anything worthwhile in attack.
Stephens, in the 74th minute, dragged his shot from the edge of the penalty area off target and substitute Pritchard fired an effort from similar distance straight at Alnwick.
But shots on goal by Powell's side could be counted on the fingers of one hand and Pritchard's late effort from inside the area in the 89th minute was too little too late for the Londoners.