The Londoners had lost on their previous five trips to Berkshire, but made a dream start as the prolific Luke Mehson collected his own grubber kick to dive over inside a minute.
Rams hit back, though, Ellis Jones with an intercept in midfield before releasing debutant Alex Mannhardt to race home down the left.
Rosslyn Park took control with two tries in four minutes, however.
Firstly, Ed Volley made a strong carry before producing a fine off-load for Charlie Walker to finish, Ed Morgan on target.
And soon after, an inside ball allowed outside centre Tom Stanton to scythe through next to the uprights.
Morgan landed again, but Rams replied as Fergus Dick produced a fine assist to send Axel Kalling-Smith over in Clubhouse Corner.
The hosts piled on the pressure before the break, but Park held out with a key maul stop to end the half.
Poor start to second half proves costly
And they then landed a sucker punch two minutes into the second period.
Despite stopping a five-metre maul, Rams conceded another penalty which star man Morgan tapped and dived over.
He added the extras and then knocked over a penalty awarded for dissent as Rosslyn extended their lead to 17 points.
There was little between the sides as the game wore on, but Rams were unable to convert the few opportunities they had in their opponents’ 22.
And the game was effectively up seven minutes from time as Max Fraine rode a maul over, Luc Smith converting.
Rams grabbed a late consolation score through Zach Clow, Mike Cooke converting, but it was too little, too late.
Defeat leaves Rams seventh in the table ahead of next week’s final game of the season against visitors Sedgley Park.
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Final Score: Rams 19-36 Rosslyn Park (Half-time: 12-19)
Scorers
Rams
Tries: Mannhardt 11, Kalling-Smith 26, Clow 77
Conversions: Lamb 27, Cooke 78
Rosslyn Park
Tries: Mehson 1, Walker 14, Stanton 19, Morgan 42, Fraine 73
Conversions: Morgan 15, 20, 43, 74
Penalty: Morgan 51
Star Man: Ed Morgan (Rosslyn Park)
Referee: Alan Chandrachud
Attendance: 815
Rams
(15-9, 1-8) Clow, Kalling-Smith, Jones, MacRae, Mannhardt, Lamb, Hoadley; Harris, Austin, Baker, Stapley, Stone, Dick, Tull, Bicknell ©
Replacements: Marshall, Marris, Lomas, Elston, Cooke
Rosslyn Park
(15-9, 1-8) Walker, Volley, Stanton, Kennaugh, Mehson, Morgan, Fenley; Cade, Piper, Kennison-Cook, Cleet, Bell, Spencer, Blackmore, Ledger
Replacements: Fraine, Wade, Gillanders, Mulchrone, Smith
