Following their El Clásico triumph over Barcelona, Los Blancos maintained their momentum with an impressive first-half performance that effectively settled the contest before the interval.
Mbappé opened the scoring from the penalty spot in the 11th minute before Bellingham doubled the advantage ten minutes later. Diomande then produced a spectacular finish in the 36th minute to complete the scoring.
The victory extended Real Madrid's winning streak to six matches across all competitions and kept them within three points of LaLiga leaders Barcelona. <Cite refs={["turn604584news7","turn604584search1"]}/>
Mbappé gives Madrid an early advantage
Real Madrid started brightly and almost took the lead when Bellingham's close-range header was saved by Racing goalkeeper Julen Agirrezabala.
The breakthrough arrived in the 11th minute after Mbappé was brought down inside the penalty area by Matteo Prati.
The French forward stepped up and confidently converted the resulting spot-kick to give the visitors a 1-0 advantage.
Racing attempted to respond, but Thibaut Courtois produced an important save to deny Iker Luque and preserve Madrid's lead.
Bellingham doubles the advantage
Madrid continued to threaten and extended their advantage in the 21st minute through Bellingham.
Arda Güler produced an excellent pass to release the England international, who raced towards goal, rounded the advancing Agirrezabala and calmly finished into an unguarded net.
The goal was Bellingham's 50th for Real Madrid, underlining his importance to the Spanish giants.
Güler also came close to getting on the scoresheet, but his effort was comfortably dealt with by the Racing goalkeeper.
Diomande scores spectacular third
Real Madrid completed their first-half scoring in the 36th minute through a stunning strike from Yan Diomande.
Following a corner, the ball fell to the forward outside the penalty area, and he unleashed a powerful first-time volley that flew into the top-left corner.
It was a spectacular finish that left Agirrezabala with no chance and gave Madrid a commanding 3-0 lead heading into half-time.
Racing fail to find a response
Racing Santander showed greater attacking intent after the restart as they attempted to reduce the deficit.
However, Madrid remained organised defensively and restricted the hosts to limited opportunities.
Mbappé came close to adding a fourth when his effort struck the post, while Bellingham also threatened again.
Racing were awarded a penalty in the 71st minute after an apparent handball by Aurélien Tchouaméni, but the decision was overturned following a VAR review, which established that the contact was accidental.
Bellingham thought he had scored again in stoppage time, but his effort was ruled out for offside.
Madrid eventually saw out the contest to secure all three points.
Real Madrid maintain pressure on Barcelona
The result extended Madrid's winning run to six matches in all competitions and kept them three points behind Barcelona in the LaLiga title race.
For Mourinho, the victory represented another encouraging performance from a side showing improved attacking confidence and collective organisation.
Real Madrid will now turn their attention to their next assignment as they continue their pursuit of the Spanish league title.