Spanish defender Calderon broke the deadlock in first-half stoppage-time with a fine left-foot finish after good link-up play with striker Glenn Murray.
Winger Noone, a recent signing from Plymouth, settled the issue three minutes after replacing Radostin Kishishev with a superb individual goal 13 minutes from time.
Colchester finished with 10 men with the late sending-off of defender Pat Baldwin for two bookable offences.
Colchester came closest when Brighton's Danish keeper Casper Ankergren denied a goalbound effort from Andrew Bond before striker David Mooney was narrowly off target from outside the area.
The victory extended Brighton's lead at the top of League One to six points.