A solitary goal from substitute Hal Robson-Kanu saw the Baggies make it four wins from their last five games at the Riverside Stadium.
In what proved to be a keenly contested clash, both teams created good opportunities to open the scoring.
Filip Krovinovic, Jake Livermore and Matheus Pereira all had chances after meeting cut-backs from Grady Diangana.
For Boro, Sam Johnstone made impressive saves to deny Britt Assombalonga and George Saville.
In the end, though, Bilic's side managed to grind out the victory - with the result delighting the head coach.
"Middlesbrough are a massive club, good players, two legends on the bench in Robbie (assistant boss Robbie Keane) and Jonathan (manager Jonathan Woodgate)," Bilic said.
"We knew they were going to enter the game with confidence.
"Unfortunately, we didn’t score from a couple of opportunities and they had that spell - a few corners, a few tackles, a few shots from outside the box.
"You could feel it, they were raising their game and the crowd got very lively.
"It became difficult. We were okay in the first half, I wasn’t that happy.
"We made some changes of attitude in the second half and we improved a lot.
"It wasn’t easy to score because they were defending in numbers, but with more quality and more quantity of attacks - we were getting the second balls and attacking again and again.
"If you have players around the box and in the box, turned towards their goal, sooner or later you’re going to come into a good opportunity, or they’ll make a small mistake or both.
"That’s exactly what happened from the quantity of our attacks."
Bilic continued: "It was well deserved. We’re delighted, especially after the international break.
"There are always little question marks, how are they going to get their focus back? Cardiff seems to be ages ago and you want to continue how we finished.
"If you add that it’s Middlesbrough, if you add that it was a clean sheet, if you add that a striker scored, it makes it a great win."
Bilic confirmed Matt Phillips, who travelled with the team to the North East, missed game with a shin problem.
But he expects him to be back for Tuesday's visit of Barnsley.
"He (Phillips) doesn’t remember a kick, it’s not a big thing, Bilic added.
"He’s going to do a scan tomorrow. It’s his shin.
I expect him to be ready for Tuesday night."