After looking bright in the early stages, City - without their FIFA World Cup stars - conceded a 27th-minute penalty when Dedryck Boyata bundled Gary Harkins to the ground.
Harkins - beginning his third spell at Dens Park - dusted himself down to assume responsibility for the spot-kick and, despite seeing his initial effort saved by City debutant Willy Caballero, the midfielder was on hand to fire home the rebound.
The Scottish Championship winners continued to press and were rewarded seven minutes before the break, with the unfortunate Boyata at the centre of the action once again.
Trialist Luka Tankulic climbed well to head goalwards, but it was a heavy deflection from the Belgian centre-back that diverted the ball beyond Caballero.
City boss Manuel Pellegrini elected to make nine changes at the break - including the withdrawal of new signing Fernando - and the Premier League side could have pulled a goal back two minutes into the second period.
Substitute Bruno Zuculini got his head to a cross from the right, but the Argentine failed to get enough purchase on his close-range effort.
City rarely looked like turning the result around, despite the introduction of the likes of Alvaro Negredo and Samir Nasri, and Pellegrini will no doubt seek improvement when they face Hearts on Friday.
