The unbeaten run came to an end on Saturday as the side travelled to Renfrewshire light in numbers but hungry to get another positive result.
And the visitors managed to take the lead shortly before the break when Ali Graham beat a home defender to a knockdown before volleying into the top left corner of the net.
However, the hosts levelled the Hills Solicitors Championship tie, converting from the penalty spot, and then made it 2-1 moments later following a free kick from the edge of the box.
Pushing for the equaliser, Rhu did have the ball in the net when Livingston headed in from a corner.
But the referee failed to spot the ball crossing the line and the goal was not given.
Linwood made it 3-1 five minutes later when the away side failed to stop a defender who ran from his own half to cross into the box.
A late push from Rhu reduced the deficit when Charlie Cook chested down a cross, turned and volleyed into the top right.
The match finished 3-2 to Linwood in what was branded a “fair result” by a Rhu spokesman, who added: “We weren’t at the races today but still a fantastic run the boys have been on and we go again next week.”
Rhu are next in action on Saturday, March 8 against title challengers Cambuslang Red Star; kick off at Hermitage Academy is scheduled for 2pm.
Rhu recently secured sponsorship from Royal Mail, with a full set of home kits and training tops supplied through the Kits 4 Kids programme.