Ramos kicked 10 points and set-up a try in humid conditions in South Africa in the six-time champions' penultimate group game in Pool 1.
Despite Toulouse's hard-fought win over Siya Kolisi's side, Bordeaux-Begles top the standings after hammering 2020's champions Exeter 69-17 in England.
Both French outfits are odds on to claim home games in the next round on April 4-6.
At Kings Park, Toulouse led 13-3 at the break in a game billed as a re-run of 2023 Rugby World Cup quarter-final.
Toulouse's Antoine Dupont was France captain two years ago with the Sharks' No 8 Kolisi skippering eventual winners South Africa.
France lock Emmanuel Meafou powered over after a Dupont pop pass, and eight points from Ramos' boot gave the visitors the lead at half-time.
Three minutes after the interval Ramos showed his class in setting up Scotland winger Blair Kinghorn with a smooth out the back door pass.
Ramos added the touchline conversion before centre Jurenzo Julius claimed a 67th consolation for the Sharks.
In Exeter, France winger Louis Bielle-Biarrey continued his good form this season crossing twice in statement win for Bordeaux-Begles.
The visitors claimed another nine tries, including a hat-trick from Damian Penaud, giving France head coach Fabien Galthie a boost before naming his Six Nations squad on Wednesday.
Earlier, the Stormers eased past Sale 40-0 in Pool 4 of the Champions Cup on Saturday to claim their first points of the season in the competition.
South Africa fly-half Manie Libbok scored 13 points for the hosts in Cape Town to keep their hopes of a last 16 place alive after having lost their opening two games.