Goals from Cauley Woodrow, Jacob Brown and Alex Mowatt did the damage at Home Park. Victory put Stendel’s ambitious charges in the driving seat for automatic promotion.
Portsmouth won 2-1 earlier in the day against Coventry, but a third successive victory for the Tykes leaves them two points ahead of their promotion rivals.
Pompey still have a game in hand on the Tykes in what is proving to be an enthralling finish to the season.
“We controlled the game and had a lot of chances,” said Stendel. “We were very good and deserved to win more than 3-0. I really enjoyed the way we played. We had a lot of chances to score in the second half, but unfortunately we couldn’t.
"But there’s a lot of pressure on our team at the moment to win our games. We just need to win our games now and see what happens.”
Woodrow fired them ahead in the 15th minute, his sweet left-foot strike too good for goalkeeper Kyle Letheren.
Brown doubled the lead six minutes later with a clinical finish. A third goal in 13 crazy minutes, this time a fine finish from Mowatt, effectively secured victory as the Pilgrims slumped to a fourth successive defeat.
Plymouth Argyle: Letheren, Threlkeld, Edwards, Jones, Sawyer, Fox (Ness 80), Songo’o, Carey, Sarcevic, Lamerias (Anderson 80), Taylor (Fletcher 80). Unused substitutes: Macey, Canavan, Ainsworth, Smith-Brown.
Barnsley: Davies, Williams, Pinnock, Lindsay, Pinillos, McGeehan, Mowatt, Brown, Bahre (Hedges 79), Thiam (Moore 69), Woodrow (Styles 79). Unused substitutes: Fryers, Walton, Green, Jackson.
Referee: Steve Martin (Staffordshire).