An exhaust system (38) for use with an engine (10) is disclosed. The exhaust system may have a first treatment device (42) situated to receive a flow of exhaust and convert a first constituent of the exhaust to a second constituent, and a second treatment device (44) located downstream of the first treatment device to reduce the first and second constituents. The exhaust system may also have a sensor (54) configured to generate a signal indicative of one of a temperature and an oxygen concentration of the exhaust, and a controller in communication with the sensor. The controller may be configured to vary the other of the temperature and the oxygen concentration based on the signal such that a desired amount of the first constituent is converted to the second constituent by the first treatment device prior to reduction by the second treatment device.