Goals from Mo Besic and Britt Assombalonga did the damage despite David Nugent's late penalty for the hosts.
Boro remain fifth - four points clear of seventh-placed County - and can confirm their spot in the top six with victory over Millwall next weekend.
"It was a smashing performance," said manager Pulis.
"We created some wonderful chances, and we've got to hit the target and make sure the goalkeeper makes saves.
"We've got to kill the game, but our football at times was excellent.
"The only disappointment was that 20-minute spell in the second half where I thought we could have scored more goals because that would have killed the game.
"We have to be a little more clinical but I thought we played really well today.
"I can't give the players any more praise because Derby gave us a proper game.
"We've got a tough game against Millwall next week so we've got to dust ourselves down and make sure we take the good stuff out of this game.
"It's tough game after tough game - but that's what this league is."
Hesitant defending from the hosts allowed Middlesbrough to open the scoring on 20 minutes when Besic placed a shot beyond Scott Carson and into the bottom-left corner.
Derby created a clutch of chances thereafter but it was Boro who got the crucial second on 70 minutes.
Adama Traore dashed down the right flank and fed the simplest of balls into the path of Assombalonga, who lashed past Carson.
Derby were given a lifeline in stoppage time when Daniel Ayala tugged Curtis Davies in the box, with referee Lee Probert pointing to the spot.
Nugent tucked home the resulting spot-kick but it proved to be too little, too late.
Derby boss Gary Rowett said: "I thought it was a much-improved performance.
"We've got to the point where it's now do or die.
"Against a Tony Pulis side, once you allow that first goal to come in, then it's difficult because you allow them to counter-attack and especially with a player like Adama Traore.
"I didn't think we deserved to be 2-0 down if I'm honest, but we didn't defend well for two moments and there were lapses in concentration.
"I can't fault the players' desire and effort today.
"They were trying as hard as they could to make something happen.
"I feel like a broken record for the last 10 weeks but we're in the same position we were in before the game.
"We've got to step up and perform and while today was better, it wasn't quite enough ultimately."