The British sportsman beat defending champion Novak Djokovic 7-6, 7-5, 2-6, 3-6, 6-2 in the Men's Final in New York in a dramatic match which lasted almost five hours.
Murray played in front of a star-studded crowd which included fellow Scot Connery, as well as The Amazing Spider-Man star Andrew Garfield, Sir Patrick Stewart, Jon Hamm and Spacey.
After the match, Connery paid tribute to the tennis ace and urged him to keep playing, telling reporters, "Of course the win is huge especially for him and I would imagine that he'll have at least six more. And I hope he'll stay with (coach Ivan) Lendl and get him to the next level."
Social networking website Twitter.com was also flooded with congratulatory messages for Murray, with Spacey writing, "Congratulations Andy Murray on your well deserved, brilliant win at US Open. I cheer your victory & everyone back home is so happy for you!"
British rockers Coldplay added their own tribute, writing, "Andy Murray Massive congratulations. What a champion," while fellow musicians Duran Duran wrote, "Congratulations Andy Murray, well done."
Actor Russell Crowe hailed Murray as a "champion" and Scottish DJ Calvin Harris was delighted to see his countryman win the grand slam title, adding, "Andy Murray you absolute Scottish hero. Scottish tennis legend."
British actor Simon Pegg sent a message to Murray and also noted Tuesday's poignant date of 11 September (12), marking 11 years since the 9/11 terrorists attacks which devastated the Big Apple: "Many congrats to Andy Murray in New York this morning and much love to New York City too while we're at it."