The Steamers won 15-66 to 1-43 away from home in the round five clash, led by a big 27-13 win in skip Robyn Thomassen’s rink.
Marilyn Stephenson skipped Moama to a 22-13 win in her rink, while the final rink resulted in a 17-17 draw.
Moama will travel to take on second-placed Deniliquin in round six, while Rich River will play Echuca at Echuca Bowls Club.
Deniliquin proved far too strong for Mathoura in their clash, winning 14-72 to 2-48.
Deniliquin bowlers Mark Quor and Conway Bovell skipped their respective quartets to 25-15 and 27-8 shot wins respectively, while Mathoura salvaged some success with a 25-20 shot win in the rink led by Jason McCloy.
Round six will see Deniliquin take on undefeated Moama at home, while Mathoura will travel to take on Rochester.
Rochester were comprehensive victors against Echuca on Tuesday, claiming a 13-70 to 3-48 win.
With one rink ending in a 19-19 draw, and another in a one-shot win for Echuca, the difference was the Rochester line-up of Kaye Barker (skip), Glenda Bancell (lead), Leigh Milgate (second) and John Weeks (third).
The foursome routed Echuca 33-10, which ultimately proved far too big an advantage for the home side to overcome in other rinks, handing Rochester the overall win.
Rochester will host Mathoura in the round six match-up, while Echuca will host Rich River.
Division Two
Stanhope recorded a massive win over Rochester, claiming victory 16-84 to 0-35 to move into third place on the ladder.
Rich River also earned an emphatic win, accounting for Ky Valley View 16-85 to 0-41, while Deniliquin RSL beat Echuca 14-66 to 2-44. Moama had the bye.
Division Three
Deniliquin RSL continued its unbeaten start to the division three season, getting the job done against Lockington 14-40 to 0-33.
Moama Green also had a strong win over Rochester, triumphing 14-43 to 0-33, while Rich River swept Elmore to win 14-38 to 0-33.
Echuca narrowly beat Tongala Red 12-36 to 2-35, while Tongala Yellow accounted for Mathoura 12-33 to 2-30, and Deniliquin narrowly beat Moama Black 12-35 to 2-34.