The 25-year-old French striker was hardly active in the opening frame as Real Madrid battled to establish a rhythm against the well-prepared Gian Piero Gasperini team.
But Real changed their fortunes after the interval, with Federico Valverde scoring the first goal after Vinicius Jr.'s pass.
Mbappe doubled Real Madrid’s lead as Atalanta started to fade, racing onto Jude Bellingham’s pass and firing a shot into the top corner.
Initially, Atalanta appeared to be the more proficient team as Marten de Roon’s shot deflected off Eder Militao and hit the Real crossbar.
And with Mbappe operating in a central role and Bellingham deeper in midfield, Rodrygo’s effort on the stroke of half-time, which hit the Atalanta bar, was the best Real had to offer.
However, Carlo Ancelotti’s side went through the gears after the interval and by the time Mbappe was withdrawn late on, last season’s Champions League winners looked comfortable winners against the Europa League holders