Watson opened the scoring in the 25th minute from the penalty spot after Reds goalkeeper Heinz Muller had upended Victor Moses and converted a Nick Carle cross on the hour to double that advantage.
Warnock believes there are more goals to come from the 23-year-old, especially if Moses, Craig Beattie and Paul Ifill continue to perform as well.
He said: "The three forwards were superb and without their movement Ben couldn't do what he has been doing.
"Ben is Ben - a top-class player at any level - and because the front three are playing well it has given him a new lease of life.
"We have been saying he can score goals if he believes in himself and with Shaun Derry back to form he and Nick Carle have been getting in the box. It was good to see him get a couple today."
Watson is currently refusing to sign a new contract, and Warnock was unable to shed any light on his prospects of a re-think. He said: "Does night follow day? I haven't got a clue."
Substitute Shefki Kuqi netted the third with eight minutes remaining by lofting the ball over the exposed Muller.
Palace goalkeeper Julian Speroni claimed an assist as his long punt upfield had been missed by the Barnsley back-line - just as it had for the penalty.
Barnsley manager Simon Davey admitted his side had been second best all afternoon.
He said: "Two goals came from the goalkeeper's kick, which was disappointing, but we were out-fought and out-played and that was not acceptable.
"Not much went for us in their penalty box but I'm not going to complain that we should have had a penalty because we were beaten by a better side.
"We had a lot of possession and created chances but never put them away and our passing wasn't as it should have been."
Davey is under pressure as the Reds remain in the relegation zone and that will intensify if they lose at home to neighbours Sheffield Wednesday on Tuesday night.
Davey is confident his players will respond to that challenge and also against Bristol City on Saturday, with both games at Oakwell.
He said: "We won't need to motivate them for that. We have two home games now so it's the ideal recipe to bounce back on Tuesday and Saturday. Let's get six points at home."