The Tykes enjoyed a 2-0 win over Bristol City thanks to first half goals from Carlton Morris and Michal Heilik.
The victory meant they have only suffered one defeat in their last six matches and are within two points of safety.
However, Barnsley face a tough trip across Yorkshire to Bramall Lane this weekend, with Sheffield United vying for a place in the top six.
If the visitors can snatch a win against the promotion-chasers then they could jump out of the relegation zone, however the following fixture against Reading will also be a good chance to boost their survival hopes.
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However, Barnsley face a tough trip across Yorkshire to Bramall Lane this weekend, with Sheffield United vying for a place in the top six.