Spurs took the lead after 27 minutes in their first match back after the COVID-19 outbreak.
Steven Bergwijn collected a loose ball just inside the Man Utd half and drove into the box before unleashing a powerful shot that David De Gea was unable to keep out.
The Man Utd goalkeeper tipped Son Heung-min's header over shortly after as it remained 1-0 at half-time.
Lloris produced a superb fingertip save to deny Anthony Martial with the visitors boosted by the introduction of Paul Pogba, who was making his first Premier League appearance since December.
The Frenchman won a penalty with 10 minutes remaining after showing great skill before being fouled by Eric Dier.
Fernandes converted to equalise and Ole Gunnar Solskjaer's side were awarded a second spot-kick before the decision was overturned by referee Jonathan Moss following a review by the Video Assistant Referee.
United remain fifth on 46 points, four clear of Spurs in eighth.
Spurs: 23 Jun v West Ham (H)
Man Utd: 24 Jun v Sheff Utd (H)