Sedgwick produced a sparkling first-round winner over York City and then repeated the performance to kill off Phil Parkinson's Colchester.
The U's misery was compounded in the dying seconds when Liam Chilvers was red carded after bringing down striker Martin Butler who was through on goal.
The Millers' winner came after 22 minutes to settle Moore's team as they shook off a dismal start to the league season that has left them floundering third from bottom of the first division.
Andy Monkhouse - recalled after being axed for two games - forced a low cross towards Butler and although he failed to connect Darren Byfield picked up the loose ball and set up Sedgwick for a blistering low drive from 15 yards.
But Colchester, unbeaten in their last six matches, came close to upsetting Rotherham before the goal.
Rowan Vine's trickery on the left flank had Chris Swailes struggling and his pull back triggered Joe Keith's shot, only for keeper Mike Pollitt to save with his legs.
And when Vine found space again on the left Pollitt had to drop smartly to block his shot before Shaun Barker headed out a dangerous cross from Bobby Bowry.
Ex-West Ham man Scott Minto created a chance for a second Rotherham goal but Monkhouse volleyed over, before the winger found space only to shoot straight at Simon Brown.
Five minutes from the end a save from Brown cut out Byfield's header after Carl Robinson picked him out with a free-kick, leaving Chilvers' dismissal as the only meaningful act of the match remaining.
Rotherham: Pollitt, Shaun Barker, Swailes, McIntosh, Minto, Sedgwick, Talbot, Robinson, Monkhouse, Byfield, Butler. Subs: Jones, Robins, Hurst, Warne, Richard Barker.
Colchester: Brown, Keith, Chilvers, Alan White, Baldwin, Stockley, Izzet, Bowry, Fagan, Vine, Duguid. Subs: Pinault, Gerken, Coote, Hadland, Halford.
Referee: T Leake.