First-half goals from re-signed midfielder Gary Harkins and trialist Luka Tankulic were enough to see off Manuel Pellegrini’s side at Dens Park, which included new goalkeeper Willy Caballero and midfielder Fernando.
Cabellero, whom Pellegrini signed from his former club Malaga last week, saved a penalty from Harkins that rebounded back for the recent signing to fire home the opener.
And 10 minutes later Tankulic, a former Borussia Dortmund youth, smashed in the second via a deflection off Dedryck Boyata.
An agitated Pellegrini made nine changes to the team at half-time, with only £4.4million Cabellero and Wales midfielder Emyr Huws staying on the pitch, but they were unable to go better than Stevan Jovetic’s chance just before the break, which he squandered against the side-netting.
Striker Alvaro Negredo and midfielder Samir Nasri, who both missed out on the World Cup with Spain and France respectively, missed with half-chances in the second period but, other than those, City struggled to create.
Dundee, meanwhile, will have been delighted with the return of goalscorer Harkins, who has begun his third spell with the newly-promoted Scottish Premiership side.
Harkins first signed for Dundee in 2009 and enjoyed a successful two-year spell in which he scored 22 times in 76 appearances, before signing for Kilmarnock. He then returned for a brief spell in 2013 and has signed again from St Mirren last month.
Dundee are taking a close look at 23-year-old Tankulic ahead of a possible contract for the German-born Croatian and he will have done himself no harm with an impressive performance and a well-taken goal.
Tankulic is a striker, most recently at Dortmund’s Bundesliga rivals Wolfsburg, where he played for Wolfsburg II further down the German leagues, after a stint with Mainz.
Manchester City’s next pre-season friendly is against Hearts on July 18 before they travel to the USA to face Sporting Kansas City.