Vaz Te blasted in a stunning effort from the edge of the area straight from kick-off to put the Tykes ahead and register their fastest ever goal at Oakwell.
In an open game, Palace levelled when Jermaine Easter capitalised on some sloppy defending to poke home in the 33rd minute and then they could have led through Darren Ambrose.
But Barnsley were dominant after the break and Vaz Te had the final say as he finished coolly after Jacob Butterfield's effort had been spilled with 13 minutes remaining.
The three points saw Barnsley make it five wins out of six as they leapfrogged Palace, who are now without a win in seven league games.
If Keith Hill's side thought they had used up their allocation of spectacular goals in Saturday's thrilling 4-3 win at Peterborough, they were mistaken as it took less than 10 seconds for them to produce another and leave those who had made it into their seats in time stunned.
Vaz Te received the ball on the left straight from Butterfield's kick-off, advanced to the angle of the penalty area and then crashed an unstoppable effort into the top corner past a helpless Julian Speroni.
The Portuguese forward had plundered one in from similar distance in that victory at London Road, but this was an even better effort and he missed out on breaking a Football League record for fastest goal by three seconds.
That early strike set the tone for an open game and Barnsley should have doubled their lead close to the half-hour mark as on-loan Nile Ranger, making his home debut, burst through on goal but his placed shot went the wrong side of the post.
And they nearly paid the price at the other end as Palace came within inches of levelling, but Glenn Murray saw his header cleared off the line by Bobby Hassell after Luke Steele had spilled Ambrose's free-kick.
That miss did not matter, though, as five minutes later the visitors did equalise when Easter took advantage of Stephen Foster's weak header back to steal in and hook the ball over Steele.
Palace could easily have gone in at half-time in front as Wilfried Zaha hooked wide with Steele out of position and Ambrose blazed over after a fine passing move.
Barnsley started the second period much the stronger and Ranger dithered when he could have shot while Craig Davies' effort on the turn was kept out by Speroni.
The home pressure was incessant and Vaz Te flashed just wide from distance, while Davies headed straight at Speroni before seeing a goalbound effort blocked by Paddy McCarthy.
Eventually the goal came with 13 minutes left and it was Vaz Te again. He calmly slotted home from 12 yards after Speroni had parried Butterfield's testing drive.
It was no more than the Tykes merited and they saw it out to clinch a deserved three points.