Barnsley emerged from this relegation six-pointer by far the stronger side and on this evidence showed enough to suggest that they can pull away from the relegation zone.
Cheltenham, meanwhile, put in a worse performance than many home supporters could remember and now look set for an uphill battle against the drop.
Ironically it was Cheltenham who took the lead after only two minutes with a well-worked goal. Michael Duff played the ball into the penalty area where Tony Naylor produced a sharp turn and shot across the goalkeeper and inside the far post.
That was to be the home side's last shot on target of the game as Barnsley slowly took a vice-like grip on the game.
Confident in possession and well organised, they also had two strikers who were a constant threat in Bruce Dyer and Mike Sheron, both of whom cost far more than the entire Cheltenham team put together several times over.
Even so, Sheron was given a big helping hand in the 18th minute equaliser when on-loan defender Greg Strong headed a long ball from Neil Austin straight into his path. Sheron ran on to plant a straightforward shot past goalkeeper Steve Book.
The all-important second goal arrived in the 63rd minute when left wing-back Dave Mulligan delivered a deep cross for Dyer to score with a powerful header.
Midfielder Gary Jones completed the scoring in the 90th minute when he drove in from 12 yards after Sheron and Dyer had combined to set him up.
"It was disappointing to gift them a goal start but we responded well," said Tykes manager Glyn Hodges.
"We showed grit and determination but some of our play was excellent." Robins boss Bobby Gould said: "We know that we have let the supporters down and must apologise publicly.
"The players are aware that what they gave fell far short of what is acceptable."