Goals from Adam Hammill, Iain Hume and an own goal by Shelton Martis put Barnsley in the driving seat before Chris Brunt pulled one back.
The Tykes made a bright start and Hammill flashed an early warning with a 25-yard effort after three minutes that drifted wide.
And when Anderson Silva whipped in a dangerous cross from the right, Jon Macken was a fraction short of a scoring connection.
Barnsley's on-loan defender Carl Dickinson was fortunate to escape with just a yellow card after 11 minutes when he launched a reckless two-footed challenge on Roman Bednar.
A stylish move by the home side saw them deservedly take the lead after 15 minutes when Silva and Macken got in each other's way but Hammill darted in and slid a crisp shot wide of the keeper.
When a Macken header sent in Hume his low shot was saved before West Brom managed an effective attack.
Dickinson was forced to clear after Bednar had missed Robert Koren's astute cross.
And after 31 minutes the Yorkshire side stretched their advantage. Another Silva cross had the visitors in a panic. Hume's header appeared to have been clawed from over the line by Scott Carson but then the ref blew for a penalty.
Canada international Hume made no mistake from the spot, tucking home his first goal since his return from the horrific skull fracture he suffered against Sheffield United last November.
West Brom bounced back after the break and went close through Bednar and then Brunt with a 25-yard free-kick that was just wide.
But with ten minutes to go Barnsley sealed the victory when Hammill swung in a dangerous cross from the right and West Brom defender Martis turned the ball past Carson for the third.
Brunt hit back with a spectacular consolation when he smashed in a stunning 25 yarder but it was too little too late for the Baggies.