Rangers could have gone ahead after just a few minutes when Maurice Edu burst into the box, messed things up and then went down under a challenge from Saints keeper Chris Smith. There were appeals for a penalty but, despite this being Rangers, it wasn't given.
However, a dubious free-kick after ten minutes gave Rangers the lead, Burke's set piece being headed home by the unmarked McCulloch.
The Saints defence continued to look dodgy and a mix-up between Smith and McAusland almost let Burke in, but like Edu he screwed up and Smith turned it behind for a corner.
There was a defensive mistake at the other end when McCulloch messed up and let in Craig Dargo, but as usual the striker failed to take the chance and Rangers escaped at the expense of a corner.
Saints started brightly in the second half and Andy Dorman played a superb pass in midfield. Unfortunately, it went straight to Burke and he charged up the park before unleashing a superb shot past Smith to as good as wrap up the points.
Saints continued to show an unwillingness to shoot along with some terrible passing, while there was a bit of booing from the home support when Rangers subbed Barry Ferguson on his return from injury.
The visitors could have had a few more and they added another in the dying moments when Rory Loy slotted a shot past Smith.
Overall, a very poor performance with the likes of Dargo and Dorman doing their chances of a first team start no good at all. Tonet was also incredibly poor and is looking like a terrible signing, while even Jim Hamilton - who has done well for the first team this season - was below par.