The four-team tournament, which also includes Arsenal and Atletico Madrid, began with a minute's applause for Sir Bobby Robson, who died on Friday, aged 76.
The tribute to the former England manager was immaculate with the travelling Scottish fans joining in enthusiastically.
But the football served up by both sides was, for much of the game, typical of a pre-season affair.
The Scottish side were certainly not outplayed by their French opponents but a sharper cutting edge would have earned them a greater margin of victory.
In the sixth minute Kenny Miller almost outwitted Gregory Coupet in the PSG goal but his attempt to curl the ball around the keeper fell the wrong side of the upright.
PSG then enjoyed the better of a lacklustre opening half.
The main threat to the Scottish side's defence came in the form of the stocky striker Mevlut Erding.
In the 10th minute, Erding headed over the bar from six yards and was clearly disappointed that he failed to test Neil Alexander in the Rangers goal.
The hard-working striker then sent an angled drive just wide of Alexander's right-hand upright in the 33rd minute but squandered his best chance of the half six minutes later.
Former Chelsea midfielder Claude Makelele, who had an exemplary game in front of the back four, sent Erding clear with a delightfully executed lob.
Such was the quality of the pass, that the ball even bounced invitingly for Erding to chip Alexander on the edge of the six-yard box.
Unfortunately for Erding, the quality of his finish failed to live up to that of Makelele's pass and his lob ended up on top of the netting.
The second half saw Rangers enjoy much more of the possession and they almost opened the scoring early on when Kyle Lafferty's header rebounded back off the right-hand post.
Coach Walter Smith made a myriad of substitutions on the hour and the Scottish champions finally broke the deadlock in the 75th minute.
A corner from Pedro Mendes was headed into the net by defender Madjid Bougherra via the underside of the crossbar and the back of Makelele.
The PSG captain just failed to prevent the ball from going over the line much to the delight of the Rangers supporters.
Rangers almost increased their lead in the 81st minute when substitute Kevin Thomson forced Coupet to tip his 25-yard free-kick around the post.
Smith's side were now well on top with man of the match Mendes continually surging forward in search of a second goal.
The French side offered little in terms of attacking football in the second half with Alexander spending much of the latter half of the game as an interested bystander.
But Smith will have been encouraged by his side's performance as they look forward to a clash with Arsenal on Sunday and a looming Champions League campaign.