Premier League champions United saw off Primera Division side Valencia 2-0 at Old Trafford.
Wayne Rooney opened the scoring early in the second half before 19-year-old Tom Cleverley wrapped up the victory.
Rangers overcame cash-rich Manchester City 3-2 in an entertaining friendly match at Ibrox Stadium.
Nacho Novo opened the scoring before goals from Stephen Ireland and Martin Petrov turned the game on its head.
Kenny Miller restored parity for Gers before a striker from David Weir sealed the victory for Walter Smith's team.
Liverpool saw off FC Lyn 2-0 in Oslo ahead of the new Premier League season.
The Reds were in action for the first time since Xabi Alonso's move to Real Madrid and the announcement that a fee has been agreed for Roma's Alberto Aquilani.
Andriy Voronin, who spent last season on loan at Hertha Berlin, opened the scoring for Liverpool on 45 minutes.
Rafa Benitez's side sealed the victory through French striker David Ngog, who bagged on the hour mark.
The only concern for Benitez came when Spain winger Albert Riera was forced off injured.
A Tottenham XI slumped to a 4-1 defeat against Crawley Town, while Blackburn's clash against Hibernian ended in a 0-0 stalemate.
Birmingham City suffered a disappointing 3-1 defeat against Tamworth, while a West Ham XI lost 1-0 to Bishop's Stortford.
Elsewhere, Sunderland were comfortable 4-1 winners in their encounter versus Durham City.