They were on the back foot for much of the game but they defended superbly as they restricted Tranmere to a handful of opportunities.
It was a first defeat in 12 matches for the Merseysiders.
The decisive goal came in the 16th minute following a short corner.
Chris Shuker crossed for Heckingbottom to power a header into the bottom right-hand corner of the net.
Stephen O'Leary was excellent in the Tranmere midfield and tested Tykes keeper Nick Colgan with an excellent 30-yarder in the 56th minute.
Rovers substitute Steve Davies also brought a good stop from Colgan in the 69th minute but generally Barnsley's defence was in control. Skipper Bobby Hassell superbly marshalled their back four with excellent support from Heckingbottom.
There was also a five-star show from Barnlsey midfielder Shuker and the visitors almost added to their lead late on when Antony Kay had a shot blocked while a Heckingbottom header was saved by Dino Seremet.
Tranmere newcomer David Raven and skipper Mike Jackson collected cautions and the latter now faces a suspension.
Barnsley's Tommy Wright and Danny Nardiello were also cautioned in a disappointing clash.