Lorenzo Pellegrini and Alexis Saelemaekers netted the goals in eight first-half minutes which gave Roma the points in a fraught atmosphere at the Stadio Olimpico in Rome.
Ranieri’s team are up to 10th on 23 points, still 12 points behind Lazio who sit in the final Champions League spot but now with some breathing space from the relegation zone.
Six points separate Roma from Lecce, who sit just inside the bottom three and drew 0-0 with Genoa earlier on Sunday, as Ranieri slowly gets the capital club going back in the right direction.
Roma were in such disarray when the 73-year-old became their third coach of the season in November that relegation was not beyond the realms of possibility.
But after an encouraging draw at AC Milan, Sunday’s display was another sign that a talented squad is starting to express itself.
Roma did not have it all their own way however and were camped in their own half after the break as Lazio pushed hard to get back into the match.
Valentin Castellanos and the impressive Nuno Tavares both went close to pulling a goal back while Loum Tchaouna’s scuffed finish looped onto the crossbar just before the hour mark.