Paul Pogba opened the scoring from 12 yards early in the game, with Shaw firing United to three points late on with a smart finish into the far corner of the goal. Jamie Vardy scored a consolation for Leicester in added time, but the Foxes left it too late to mount a comeback.
After the match, Shaw spoke to Sky Sports about scoring his first ever goal for Manchester United, claiming that he has the foundations at Old Trafford to become a household name across Europe.
"I don't want to speak too soon after one game but I've been working really hard and I want to be up there with the best left backs in the world," Shaw said, quoted by the Daily Mail. "With a great manager and great team-mates around me, I think I've got the foundations to do that here at Manchester United."
Shaw first moved to Old Trafford in 2014 after breaking onto the scene at Southampton, costing the Red Devils over £30m. However, the 23-year-old hasn't lived up to expectations and has only ever made 67 appearances for the club - equaling his tally from a two-year spell in the Saints' first team.
Shaw was set to become a free agent this summer but his contract was extended by another year, with Manchester United now having to make a decision over his future or risk losing him on a free transfer in 2019.