Smith has now won five of his eight matches since taking over the Villans to climb within three points of a play-off place.
And after the 5-5 draw with Nottingham Forest in midweek, the Villa boss was particularly satisfied to have seen his team win comfortably - and keep another clean sheet under him.
James Chester scrambled the opener in the 20th minute before Tammy Abraham grabbed the second just after the hour.
The victory was completed when substitute Glenn Whelan’s long range effort was helped in by goalkeeper Darren Randolph with seven minutes left.
Smith said: “We played very well, started on front foot, controlled possession, should have had a penalty, wasn’t given when Tammy was brought down by George Friend. We scored from another set piece, we are getting good at them and long may those continue.
“Defensively we were on the front foot. We wanted to play the game in their half. They found it difficult to break us down.
“They kept 11 clean sheets and have for a reason, so it was always going to be difficult to break them down. We got the goal in the end, we know we have the quality in the squad to then go and get a second.
“It has to be a team game. Question marks after Wednesday, five conceded, goalkeeper, defence, we had players out. I said that Wednesday was a freak. But I have four clean sheets from the eight we have played, I am happy with that.”
Middlesbrough manager Tony Pulis was less supportive of the performance of his team, knowing that an eight match unbeaten run has come to an end.
It also means that Middlesbrough, who disappointed from start to finish and only truly went close when Jordan Hugill hit the bar, are four points behind the automatic promotion spots.
Pulis said: “On the day we weren’t good enough, not bright enough. Right from the start, Marcus Tavernier ran round the wrong side of Jordan, and from that moment on we didn’t look bright enough, didn’t play as well as we can do.
“The difference against these teams, every player has to be on it. They were better than us. Full stop.
“People can have a go at Randolph, others, I am not. We look at the league, and we look at today and we got beaten badly. I can pick holes in everything, from the back to the front. I am not going to because I don’t think they deserve it.
“We have four or five games before the window opens and we have to make sure this team sticks together to get as many points as we can.
“Darren should do better in both goals but he has been fantastic, a fantastic lad as well. I have been here nearly a year, he is a great pro. They are disappointed with their performance today. We will dust ourselves down and we go again.”