After Caicedo had fired an early effort over the bar after being set up by Wright-Phillips the Ecuadorian fired City into an eighth-minute lead.
Caicedo brushed past his marker, Michael Jakobsen, on the edge of the area before firing past Karim Zaza in the Aalborg goal.
City threatened to run riot with Robinho and Stephen Ireland showing some good touches but their defence also allowed the visitors, who finished above Celtic in the Champions League group stages and knocked Deportivo La Coruna out of the last round of the UEFA Cup, hope.
Caicedo almost made it 2-0 in the 18th minute after Robinho set him up but two minutes later Aalborg went close to equalising when Kasper Bogelund sent Andreas Johansson free only for his effort to be blocked by Micah Richards.
Shay Given had to be alert to save the lively Caca's shot with his legs as Aalborg responded well after making a poor start to the game.
Nedum Onuoha headed Elano's corner wide before City doubled their lead on the half-hour when Wright-Phillips lashed a 25-yard shot into the top right-hand corner of Zaza's net.
Almost immediately the visitors nearly pulled a goal back when Thomas Augustinussen steered a shot wide when he should have hit the target.
Just before half-time Robinho created space for himself before firing a shot at Zaza's chest and the Brazilian should have had a penalty only for the referee to wave away his protests.
In the second period City sat back and seemed content to hang on to their two-goal lead. A powerful Onuoha header was only just too high before Ireland and Robinho combined well only for the Brazilian to see his effort saved by Zaza.
In the 74th minute Wright-Phillips almost added a third goal when he sliced a shot wide while Caca wasted a late opportunity to grab an away goal for Aalborg when he fired an effort past the post.