A clinical brace from striker Sam Winnall and another goal from defender Marc Roberts secured the three points at St Andrews, leaving Heckingbottom to salute a complete team performance.
The Reds boss said: “I was delighted. Obviously a clean sheet away from home is always good. We were over the moon getting one at Birmingham. It’s one of the tougher places to go to. To a man we were really professional. We carried out the same game-plan and in the end it was a well-deserved victory for us.
“Everyone contributed, and everyone has to. This is a tough league, but more often than not, if we get it right, we win. In the first half I thought we could have scored more.
“However, once we got the second, that killed the game. The third was the icing on the cake.”
Roberts glanced home Conor Hourihane’s free-kick to open the scoring shortly before half-time.
Winnall then added a couple of late headed goals - his sixth and seventh of the season - both of which were again set up by star man Hourihane.
* Sam Winnall was back to his deadly best as he registered a couple of predatory late goals.
But Heckingbottom wasn’t overly concerned about whose name was on the scoresheet.
He said: “I’m not bothered who scores the goals.Everyone wants to score the goals, but we are a team and it’s not about any individual.
“Tom Bradshaw was fantastic up there next to Sam, but I if we start getting selfish and thinking it’s all about them, we won’t get anywhere.It’s a real team effort.”
That was highlighted at the other end of the field as goalkeeper Adam Davies produced more crucial stops as the Reds secured a precious clean sheet. Davies has produced more saves than any other ‘keeper in the Championship so far this term - 70 - and his effort to keep out Clayton Donaldson in the first period was particularly breathtaking.
* Following a week of discussion regarding whether Barnsley will be able to hang on to Conor Hourihane during the transfer window, the supremely-talented midfielder turned in another wonder show.
The Irishman was in brilliant form again for the Reds, setting up all three goals.
Since promotion from League One, Hourihane has proved beyond doubt he belongs at Championship level.
Now, a number of top clubs feel he would be capable of making the step up to the Premier League.
Birmingham (4-4-2): Kuszczak; Dacres-Cogley, Morrison, Shotton, Grounds; Davis, Tesche, Kieftenbeld (Stewart, 60), Cotterill (Brown, 72); Jutkiewicz (Adams, 60), Donaldson. Subs not used: Legzdins, Robinson, Gleeson, Solomon-Otabor.
Barnsley (4-4-2): Davies; Bree, Roberts, MacDonald, Yiadom; Kent (Williams, 85), Scowen, Hourihane, Morsy; Winnall, Bradshaw. Subs not used: Townsend, Kpekawa, Evans, Janko, Armstrong, Hammill.
Referee: David Coote (Nottinghamshire).