David Templeton then added a second in the 90th minute but the Ibrox men were far from impressive.
The victory - which sends Rangers 20 points clear at the top of Scottish League One - was the first match played since Ally McCoist's team rejected a 15 per cent pay cut.
But the Glasgow giants gave little value to the supporters who braved a cold January night to make their way to Angus.
Rangers were sloppy in midfield and failed to impose themselves on a determined Loons side still buzzing from the knowledge that they are the only side to beat the Light Blues this season.
That famous win was chalked up in the first round of the League Cup when they claimed a 2-1 extra-time success.
Goalkeeper Simonsen was making his first appearance as a Rangers player after regular Ibrox number one Cammy Bell was given the night off to attend the birth of his baby daughter.
But Bell's understudy did not let stage fright get the better of him and came up with a fine reflex stop to save Lee McCulloch the indignity of scoring an own goal 10 minutes from time.
The Rangers captain had come close at the other end, too, when he hit the bar with a free-kick but it was Mohsni who settled his side's nerves when he headed home with a quarter of an hour left before Templeton fired into the top corner 60 seconds before full-time.
Rangers were well aware of the banana skin that awaited them at Station Park following August's cup shock.
Yet they still allowed Forfar space to threaten in the opening moments.
There was just three minutes on the clock when Malcolm headed onto the crossbar after Martyn Fotheringham did well to dig out a decent ball to the back post.
That close shave shook the visitors into an immediate response and only Rab Douglas' alertness prevented Nicky Law from scoring with a dipping volley.
But Rangers were neither fluid nor dominant as they struggled to settle against the Loons' industrious midfield.
There was a touch of desperation about them as they appealed unsuccessfully for a penalty after 21 minutes when Lee Wallace ran into Darren Dods in the box.
Dean Shiels was well off target after Jon Daly sent him running through on Douglas' goal and the visitors' frustration was obvious as both Sebastian Faure and McCulloch were booked inside a minute for late challenges.
Simonsen's first save as a Rangers player was a comfortable affair on 35 minutes despite the deflection on Fotheringham's 30-yard strike.
Mohsni was next to be cautioned as he got himself in a tangle trying to dribble out of defence before tripping Odmar Faeroe while Simonsen then rescued McCulloch with a smart save from Gavin Swankie's volley after the Rangers skipper put him in with a miscued clearance.
Rangers waited until just before the break to create their best opening but Douglas was down well to save from Fraser Aird's strike before blocking Mohsni's follow-up attempt.
McCoist's side could hardly have been any worse in that opening 45 minutes but did return for the second half with renewed vigour.
Forfar full-back Gary Fusco was lucky to survive beyond the 53rd minute after snapping Lewis Macleod just 60 seconds after collecting a yellow card for a foul on the same victim.
When he was replaced moments later by Mark Baxter, Loons boss Dick Campbell was clearly saving the defender from himself.
The tetchy visiting support were well beyond restless by this stage but their stresses were almost relieved when McCulloch crashed a free-kick onto the crossbar on the hour mark.
They were back at breaking point though when Baxter's apparent shove on Mohsni from a Rangers corner failed to bring a spot-kick award from referee Stephen Finnie.
But having laboured for 75 minutes, Rangers finally found the breakthrough when Mohsni out-jumped Dods to send Aird's corner into the net with the aid of the back post.
Simonsen then saved brilliantly after McCulloch got it all wrong trying to defend a corner but Templeton made sure of the victory when he fired past Douglas from 18 yards with time just about up.