Romelu Lukaku enjoyed a dream home debut, netting twice to send the Red Devils to the top of the Premier League.
Substitute Anthony Martial and Paul Pogba were also on the scoresheet in the dominant display.
And Savage is convinced United will be the team who lift the Premier League trophy next May.
He said: "Manchester United are my tips to win the title.
"Nobody can accuse United of being boring or dull today.
"Without getting carried away, it is the first day of the season, West Ham had a few new signings and were confident, but United have totally, totally destroyed them."
United were dominant throughout with Marcus Rashford hitting the post in an impressive display.
West Ham offered little in attack with Javier Hernandez not enjoying his return to Old Trafford.
Savage added: "The big word this season used at United is excitement and there was plenty of that today.
"United have put a marker down and for me they are the title favourites, and there is no reason for me to change my mind."
The Red Devils' next challenge is a trip to Swansea in the Premier League on Saturday.
West Ham will look to record their first win when they travel to Southampton.
