Los Blancos cut the gap on league leaders Barcelona to two points after the Catalans drew 2-2 at Real Betis, with Madrid having played one fewer match.
Bellingham opened the scoring before half-time and set up Arda Guler for Madrid's second, before Mbappe produced a clinical finish for their third.
Both Bellingham and defender Ferland Mendy were replaced with apparent knocks in the second half ahead of Tuesday's Champions League clash at Atalanta.
Coach Carlo Ancelotti confirmed Bellingham would be fit for the game but said Mendy had suffered a muscular injury.
After Madrid's fifth defeat across all competitions in midweek against Athletic Bilbao, having lost just twice last season, Ancelotti pledged his team would improve and they were significantly better against Girona.
"Bellingham scored his fifth goal running (in La Liga), Mbappe scored, Brahim (Diaz) did good work, Arda scored a great goal, as I said, bit by bit we will come back (to form)," said Real Madrid coach Carlo Ancelotti.
With Vinicius Junior and Rodrygo sidelined, Ancelotti selected Bellingham and Diaz in support of Mbappe.
The French forward has been the focus of criticism in recent weeks after blowing penalties against Liverpool and Athletic Bilbao, and struggling to find the form which made him a star with Paris Saint-Germain and his country.
Girona, who ran Madrid close for the Spanish title for much of last season before eventually finishing third, started the stronger and Bryan Gil fired wide, with Donny van de Beek lashing over.
Madrid settled into the game and, keeping the hosts at arm's length, began to create chances of their own.
Paulo Gazzaniga saved Brahim Diaz's fierce drive from the edge of the box as the champions clicked into gear.
Bellingham broke the deadlock after 36 minutes when Diaz's cross was blocked and the ball fell kindly to the England international, who fired home through a crowd of players.
It was Bellingham's fifth goal in his last five La Liga games, with the former Borussia Dortmund midfielder finding the form which inspired Madrid to a Champions League and La Liga double last season.
After a quiet first half, early in the second Mbappe broke through and fired wide, although the striker had handled the ball to control it and if he had scored it would not have stood.
Improved display
Madrid kept pushing and Gazzaniga saved well from Aurelien Tchouameni's header from Luka Modric's free-kick.
Los Blancos got their second in the 55th minute when Bellingham threaded through a fine pass for Guler, who rolled the ball home.
Bellingham hobbled off after sustaining an apparent knock in a challenge before Mbappe rattled home Madrid's third.
After Thibaut Courtois saved well from Yaser Asprilla, Madrid burst forward on the counter-attack.
Modric sprang the French forward, who finished with aplomb from a tight angle on the right side of the area, across Gazzaniga into the bottom corner.
Madrid beat Girona 3-0 at Montilivi and 4-0 at the Santiago Bernabeu last season and this victory was another which showed their superiority over the Catalan minnows.
Ancelotti will hope they can carry some momentum into the vital Champions League visit to Atalanta, for which Vinicius is expected to return from a hamstring problem.
Girona, eighth in La Liga after a poor start to the season exacerbated by a host of injuries, welcome Liverpool in the Champions League on Tuesday.
"If we were more accurate in front of goal it would have been different," said Girona defender Miguel Gutierrez.
"We have to continue, we have two very important games, Liverpool in the Champions League and then at Mallorca (in La Liga)."
