Goals from Jordan Hugill and Marcus Tavernier made it six games unbeaten, with Boro leapfrogging Leeds United to go second in the Sky Bet Championship, two points behind leaders Norwich.
He said: "This is a very difficult place to come, it's a very tight ground and they move the ball around really well. They are a good side so this is a very good win.
"I've been here a lot and it's not a ground you look forward to playing at under the lights, so it's pleasing that we came and did a very tight, professional job."
Pulis had special praise for striker Hugill, who gave the hosts' two young centre-backs a torrid time throughout the match.
He said: "He moved them about and gave them a very physical test and that allowed us to get others in and around him to pick up the pieces."
Alan Judge gave Brentford hope with a late goal and Pulis was unhappy with how his side dropped deeper to let the hosts back into the game.
"Once we were two up I thought we could have consolidated and looked to add to it, but we fell back a little and that allowed them to get back into the game a little which was disappointing," he said.
"But we were resilient, well organised and always posed a threat going forward, so I can't complain too much about the outcome."
Brentford head coach Thomas Frank felt his side's lack of quality in the final third cost them in a game where they dominated Middlesbrough for long spells.
But despite seeing his side slip to a fifth defeat in six, he is confident the "big heart" shown by his players will soon help turn things around.
"We dominated the game but you have to defend well in crucial situations, and although they were happy to sit back we needed to open the game up," he said.
"Middlesbrough are a big team and are favourites to go up, and we matched and were better than them for much of the game. But we also need to be more aware offensively with our final balls and decision making."