In one aspect, a pressure sensor for detecting a pressure differential between first and second fluid sources may include sensor body defining a cavity and a seal plate slidably positioned within the cavity. The seal plate may define first and second chambers within the cavity, which may respectively be in fluid communication with the first and second fluid sources. The sensor may also include a sensing element configured to detect a position of the seal plate relative to the sensor body, which may be indicative of the pressure differential between the first and second fluid sources. The sensor may further include a first spring positioned within the first chamber and compressed between a first side of the seal plate and the sensing element. Additionally, the sensor may include a second spring positioned within the second chamber and compressed between a second side of the seal plate and the sensor body.