Antonio Rudiger headed home in the 83rd minute for the record 15-time champions after Deniz Undav had levelled Mbappe's opener just seconds into the second-half.
Endrick, another Champions League debutant, wrapped up Madrid's win with a low drive in stoppage time.
Stuttgart had the better of an entertaining opening period but Carlo Ancelotti's team have a habit of grinding out victories when up against the wall and they took the three points despite the visitors' impressive efforts.
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Older hands add value
The next Rugby World Cup is three years away, in 2027, and much of the talk after the last event and now currently, has been about a number of the older guys in the Springbok squad and for how long they will continue playing for the world champions.
Stubbs happy to 'do his job'
Delivering one of the best international performances of his career, middle-order batter Tristan Stubbs (below) was relieved to carry his team over the line after guiding the Proteas to a three-wicket victory over India in the second T20 International in Gqeberha on Sunday night.
BOK WAKE-UP CALL
BE BETTER: WORLD CHAMPS MUST STEP UP THEIR GAME
Sinner cruises in finals opener
Jannik Sinner (above) got his bid for a first ATP Finals title underway with a 6-3, 6-4 win over Alex de Minaur on Sunday as former champion Daniil Medvedev lost his head during his defeat to Taylor Fritz.
Proteas women broaden the pool
NEW FACES: MULTI-FORMAT SERIES AGAINST ENGLAND
The 'incredibly tough men' will shine
India coach Gautam Gambhir yesterday backed \"incredibly tough men\" Rohit Sharma and Virat Kohli to prove their critics wrong and find form in Australia.
Dupont warns of All Black 'threat'
France superstar Antoine Dupont (right) said he was cautious of New Zealand's \"threat\" before the in-form All Blacks head to Paris on Saturday.
Gatland takes it on the chin
Warren Gatland (above) said he was unconcerned about his future as Wales coach after watching his team lose 24-19 to Fiji on Sunday in what was a record-equalling 10th successive Test defeat.
Poch prefers home-grown
Mauricio Pochettino (above) said he will not try to \"convince\" dual-nationality players to opt for the United States, insisting he wants to build a squad made of footballers desperate to represent the country.
England keen to click
ITOJE: DESPERATE TO MAKE THE FANS PROUD AGAINST THE WORLD CHAMPS
