The 20-year-old's first senior goal for the Ibrox club was all that separated the two sides in the clash at Mosset Park, which saw Nathan Sharp dismissed for the home team.
Rangers have so far failed to pick up a win on the road in the Third Division this season but, thanks to Naismith's strike, claimed a narrow victory in what could have been a tricky tie.
Light Blues boss Ally McCoist made two changes from the side that defeated Motherwell midweek for the long trip north to the Highlands. Naismith was handed his first start, while Kyle Hutton was also drafted into the starting line-up.
Forres claimed for a penalty in the opening minute for handball against Sebastien Faure but their pleas were ignored by referee Crawford Allan. Instead, it was Naismith who made the most of his opportunity when he grabbed the only goal of the game after 14 minutes.
Fraser Aird did well down the left before crossing into the box, where the ball was missed by Lee McCulloch in front of goal, before falling kindly for Naismith to rifle home. Forres could have hauled themselves level minutes later but Scott Moore just failed to connect with a teasing ball into the box and stab home the equaliser.
Aird set about trying to double Rangers' lead after the break when he dragged a shot wide shortly after the re-start, before testing the goalkeeper with a tame strike. Forres still looked dangerous and had a great chance when Allan's free-kick found Kyle Scott in front of goal and Neil Alexander was forced to block the point-blank effort with his feet.
The Highland League champions' hopes of hauling themselves back into the tie were dealt a blow after 64 minutes when Sharp picked up a second yellow card for deliberate handball.
Rangers made another switch when Aird was replaced by fellow youngster Robbie Crawford and he almost grabbed the elusive second goal. Lewis Macleod was the provider with a dangerous ball from the right and Crawford was denied only by an excellent save from Knight to force the shot over.
There was one final attempt from Forres to secure a lucrative replay at Ibrox but Graham Fraser bulleted his header inches wide with a couple of minutes to go as Rangers held on for the win.