A fourth successive Riverside success ensured the Teessiders remain in the Championship play-off spots with just nine games remaining.
For the first hour of the contest Pulis’s team showed some classy moves and clinical finishing.
After the victory the Welshman was quick to praise the style of his side’s play and request more of the same.
“We’re not wasting passing, we’re actually playing smashing football,” said Pulis.
“We want to get that ball to the three forwards.
“That’s the way I like playing; I’m not a backwards and sidewards man.
“Truthfully, I love getting the ball wide and getting down the pitch and getting the ball into the box.”
Pulis is hopeful his players can last the course as they plot a quickfire Premier League return and he knows that he possesses a potential match-winner in the form of winger Adama Traore.
He added: “The challenge is to stay in there now.
“Once they cross that line it’s up to them.
“In the next nine games we’ll see.
“I haven’t brought them in so I don’t know what their characters are like.
“They’ve been fantastic since I’ve been here – now we’ve just got to keep it going.
“We’ve got a flying winger on that right-hand side who will cause anybody problems – in any league in the world when he’s at it.
“At times against Barnsley, he was absolutely scintillating.
“We passed the ball well and got through the pitch and got lots of crosses in.
“The disappointment was that we didn’t score more goals.
“We came out after half-time and got that third goal, which, truthfully, should have killed the game.”