The victory moved the Upton Park side three points behind second-placed Southampton, who have a game in hand. And the Hammers set a club record of 12 away league wins in a single season.
Barnsley suffered a sixth defeat in their last seven league outings and were left looking over their shoulder in the hope they are not dragged into the relegation mire, especially with four of their five remaining games against play-off chasing teams.
The Tykes appear safe as they are nine points above the drop zone, but their form has plummeted and West Ham's victory was hardly in doubt after Nolan's sixth-minute goal.
A West Ham corner ricocheted off Craig Davies and left an unmarked Nolan to apply a simple finish from point-blank range.
Barnsley midfielder Stephen Dawson survived being red-carded for a two-footed tackle on James Tomkins before Maynard's lovely finish extended the away side's lead.
West Ham's pressure and persistence was the springboard of their victory and, after Maynard's closing down of Button forced the keeper into a poor clearance, Noble took advantage by chipping in.
Barnsley failed to produce any sign of a comeback, while West Ham were revelling in the space and time on the ball they were being afforded.
Left-back McCartney even got in on the attacking action and despite having his curling shot saved by Button, the keeper could only palm the ball to ex-Barnsley forward Vaz Te, who sidefooted home.
Maynard shuddered the crossbar with a long-range strike before the referee's whistle ended Barnsley's misery.
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