The former Scotland manager made no secret of his unhappiness with the Blues' tame performance in defeat at Bolton but he was encouraged by their determined response against Gareth Southgate's men.
"At Bolton our performance was insipid but against Middlesbrough we got into their faces and it paid off," said McLeish after a Stewart Downing own goal, a Mikael Forssell strike and Gary McSheffrey's late penalty had clinched three welcome points.
"Playing two strikers (Forssell and Cameron Jerome) worked for us. The tempo was high and we got the breaks which we held on to. We defended stoutly as a team and fully deserved our success.
"Our objective now is to take this form into Saturday's game against Fulham. We are hoping to pick up six points from the two holiday games and we are halfway to our objective.
"It was terrific not only to get the points but to keep a clean sheet as well. I was pleased for the goalkeeper and the defenders who take pride in these sort of achievements."
McLeish, reflecting on recent results, added: "The Premiership is an incredible league. When you look at the results over the last few weeks you realise that anyone can win. Look at Middlesbrough beating Arsenal and now we have beaten them.
"It is a hugely competitive league and not for the faint-hearted. We now have to battle with the teams in our group and get as high as possible. That is our goal and getting something from the bigger teams like Manchester United (on New Year's Day) would be a bonus.
"That doesn't mean that we do not think we can get something from these matches."
There was, however, a fair measure of good fortune about Birmingham's crucial opening goal in the 23rd minute which came about after a chapter of errors on the part of Boro.
Jerome's pace caused a problem and a frustrated Julio Arca took matters into his own hands when he blatantly shoulder charged the Birmingham striker off the ball.
Referee Mark Halsey was in close attendance and did not even need a second thought about booking the Argentinian defender and awarding a free-kick.
McSheffrey's inswinging free-kick was dramatically sliced into his own net at the near post by Downing with goalkeeper Mark Schwarzer helpless.
Middlesbrough's hopes of getting back into the game disappeared seconds before half-time. Sebastian Larsson's corner from the left was headed on by Jerome and Forssell bundled the ball home at the far post with Boro's defence in total disarray.
In the last minute Robert Huth brought down McSheffrey who converted the penalty.
Boro boss Southgate admitted the Blues had been well worth their win.
"We didn't deserve anything from the game," he said. "I thought we were very, very poor in the first half and didn't get out of the traps.
"I've heard people use the phase 'we have turned the corner.' I knew we hadn't and the evidence is there for everyone to see. There is a tremendous amount of hard work to be done.
"I think we let ourselves down because 3-0 is a very poor result. Now we have to roll up our sleeves up and work together to get ourselves back on track. We have to go to Portsmouth and do that.
"In this division you are only one result away from sliding back into problems. We had that bad result against West Ham which put more pressure on the Birmingham game.
"We let ourselves down and now have to respond. We have come through a tough run over the last few months and we must do it again."