Gayle took his tally for the season to 11 and secured the Magpies a fifth away win of the campaign as they defeated the Tykes in front of nearly 6,000 travelling fans.
The striker’s contribution pleased his manager, who said: “When you have players as clinical as Dwight, you will score goals.
“The team played well and created chances. His job is to be there, fighting with the centre-back and try to score if he gets a chance. He is on fire now, he is happy and we’re all happy.
“I made it our priority in the summer to get him and Matt Ritchie to the club.”
On the game itself, Benitez continued: “It was a very professional performance. We needed to work hard, be strong physically against a good team who were pressing and pushing us.
“We did that in the first half, while scoring in the second half where we had more time, more space and possession and we could play in a different way.
“I am really pleased as we did what we had to do.”
Burnley midfielder Jack Cork is confident his side can reach the Europa League but expects a stern test in qualifying.