It was to be a frustrating afternoon for the Rhu strike force as chances went a begging with a mixture of good goalkeeping and missed opportunities keeping the score down.
Rhu started with three up front and soon had Symington on the back foot.
David Sinclair was having a bit of joy on the right and managed to get some good crosses in but Symington's keeper did well to deal with them as Rhu came close to the opener.
Rhu did take the lead though after 20 minutes when the ball broke to David Sinclair at the edge of the box, he ignored calls for offside pushed forward and fired the ball in to the net.
Rhu kept the pressure up and it was soon two when Dougie Black met Neil Thomson's cross from the left perfectly and smashed the ball home.
No sooner had Rhu gone two up than Symington had pulled a goal back with their first opportunity.
A clearance broke to the visitors' number 10 and his first time effort came off a Rhu defender before going in off the post.
Rhu continued to press and should have had a penalty when Davie Falconer was brought down in the box, but the referee waved away the appeals.
The home side were out of luck again when Davie Falconer broke through lobbed the keeper only to see his effort come back off the crossbar.
Despite constant pressure Rhu found themselves just one ahead at the break.
This was also to be the theme for the second half with Rhu unabole to find the decisive third goal.
With just one goal advantage the game was never over and to their credit Symington forced a couple of corners near the end, but there was to be no further scoring.
Team: Heron, MacDonald, McMillan, Cheesman, Grant, Black, McColl, Thomson, Chalmers, Falconer and Chalmers. Subs Scullion, Porter, Miller, Petro.
This Saturday Rhu are at home again in a West of Scotland Cup fourth round against Central League Premier champions Drumchapel United (kick-off 1.30pm).