Brazilian midfielder Geovanni looked sharp in his first City appearance in England, while there were also nice touches from young midfield duo Stephen Ireland and Michael Johnson in the first half.
Georgios Samaras missed a great chance to open the scoring at the start of the second half but he played a part as City finally broke the deadlock in the 82nd minute.
The Greek striker swung in a cross for Bernardo Corradi to head home his 4th goal in 5 games during pre-season.
Paul Dickov then grabbed another with a neat finish in the final minute to round off City's 4th win from 5 friendlies.
The match, played at Shrewsbury's New Meadow, was arranged as part of the deal that saw Joe Hart move from the League Two club to City last summer and the England U21 keeper came on for the second half.