The 27-year-old gave referee Peter Bankes no choice but to show him a straight red card following a rash tackle on Man United forward Bryan Mbeumo just five minutes into the game.
Sanchez had looked shaky in the opening stages of the game and his decision to charge off his line and clean Mbeumo out backfired spectacularly.
As a result, the Spaniard has become the unfortunate record-holder for the earliest red card ever received by a Chelsea player in a Premier League match.
United captain Bruno Fernandes went on to open the scoring nine minutes later before Casemiro doubled their lead on the 37th.
Casemiro was then sent off just before half-time to put the two sides on a more level playing field, but despite a late Trevoh Chalobah goal, Ruben Amorim’s side held on.