McLeish brought on the on-loan Argentinian striker with 13 minutes remaining after Joleon Lescott's ninth goal of the campaign put the Toffees ahead.
And within six minutes the 21-year-old took heed of McLeish's instructions to take a free-kick on the edge of the Everton box as he drilled an unstoppable effort past Tim Howard.
The share of the spoils means Blues are now two points ahead of third from bottom Bolton and have a superior goal difference.
McLeish said: "That goal and point could turn out to be very important. It was a cruel blow to go behind. The second half performance was exceptional. We went up a gear and found another couple of per cent.
"It was only the finishing touch that let us down and some terrific stops by Tim Howard.
"I've seen Zarate on DVDs doing that at free-kicks. He practices that in training. If Sebastian Larsson had been on the pitch, he would have probably pulled rank and taken it because he has been successful from a couple already this season.
"I saw a congregation gathering around the ball and I knew at a given moment a few people fancy themselves to pop the ball over the wall and into the top corner.
"It very rarely happens so I made sure David Murphy got word that I wanted Zarate to take the free-kick and it is a beautiful finish. I think I'll claim an assist for that - a super decision putting him on!"
Everton boss David Moyes said: "I think it was a fair result. Birmingham had one or two chances in the second half but I thought when we got the goal we would hang on for the win.
"It was important goal from Joleon. He has got nine now for the season, a great return.
"We had one or two opportunities without making great chances in the first half but in the second half they upped it a bit more than we did even though we went in front."
Moyes admitted he would like to rest some of his players but injuries are preventing him from being able to adopt that course of action in the push for a European spot.
He said: "I could do with giving them a breather but at the moment we are very limited in what we have available in forward areas and in midfield we are nearly drained of resources.
"I want to make sure we finish fifth at the worst but I'll always keep trying to get fourth while it is a possibility."