After making a name for himself off the field through his campaign against child poverty during the pandemic, Rashford excelled in his day job with a trio of well-taken finishes after entering as a 63rd-minute substitute.
The England forward ran onto a first-time pass from Bruno Fernandes and slotted home to make it 2-0 in the 74th, building on the first-half opener by Mason Greenwood that made the 19-year-old forward United's second-youngest scorer in the Champions League after Wayne Rooney.
Rashford's quick feet saw him charge through Leipzig's open defense and drive in his second goal in the 78th and, after Anthony Martial made it 4-0 from the penalty spot, the France striker teed up Rashford to completed his hat trick in the second minute of injury time.
It was the heaviest loss in Leipzig's 11-year history.
United opened Group H with a 2-1 win at Paris Saint-Germain and can look forward to a double-header with Istanbul Basaksehir either side of the upcoming international break, knowing two wins could allow the team to seal qualification for the knockout stage.
A change of shape by manager Ole Gunnar Solskjaer saw United switch to a diamond formation and it worked wonders at Old Trafford, with the recalled Paul Pogba surging through midfield and setting up Greenwood for a well-taken opening goal in the 21st minute.
