While the Mandate of Heaven was a Zhou concept, the idea in imperial Chinese history was only reformulated during the Eastern Han, where it went hand-in-hand with Confucian classicism with ritual obedience from subject to Emperor.
There are plenty of ways Chinese Emperors legitimized themselves besides the 'Mandate of Heaven' concept. There is the Mencian/Confucian claim that 'the best should rule', the idea that the Emperor was literally the Son of Heaven, the idea of legitimacy coming from the ruling clan's superior Qi ('energy'), the idea that the Emperor was the representative/patron of Confucian/Chinese civilization, as well as being the main link between the earthly and the various state cults.
Anyway, I wouldn't say that the Mandate really stopped anybody from revolting against the Emperor - like prophecy, it's all too easy to cherrypick/fake various 'phenomena' (especially if they refer to nebulous things like Qi) that would justify any ruling house losing the Mandate.