Two goals in either half from Colchester United saw them progress to the Second Round of the Emirates FA Cup, with Wiredu, Sears, Jasper and McCoulsky all finding the back of the net.
Brendan Wiredu got the U's on their way, being in the right place at the right time to tap home just after half an hour, with Freddie Sears doubling the advantage with a fierce strike four minutes later.
Sylvester Jasper netted midway through the second period with a perfect curling strike, before Shawn McCoulsky put the icing on the cake with a well-taken volley from inside the area.
Hayden Mullins made two changes to the Colchester United side that beat Scunthorpe United 2-1 at the JobServe Community Stadium on Saturday afternoon.
Miles Welch-Hayes and Charlie Daniels were missing from the starting eleven, with Ryan Clampin and Junior Tchamadeu coming in to replace them.
Colchester United took their time getting into the game, but were in control for almost all of the time before they netted the opener in the tie.
Shamal George had a couple of attempts at clasping on to the ball from an AFC Sudbury free kick, but was able to find his feet swiftly to ensure that the hosts didn't take an early lead in the tie.
But the U's were back up the other end much more than the hosts and Sears, Dobra and Jasper looked too much to handle for the Sudbury back four.
Freddie Sears and Noah Chilvers both had shots that stung the palms of Blunkell, with Wiredu having a couple of attempts that flew just either side of the goal before Hayden Mullins' side found their breakthrough in the First Round match.
Brendan Wiredu was the man to break the deadlock for the U's when he snuck in at the back post to sidefoot beyond the 'keeper and snatch the lead for the visitors. The ball was flicked on at the near post with Wiredu in the right place to force home the advantage.
And the U's doubled their lead just four minutes later, with Freddie Sears finding the back of the net this time. Wiredu laid the ball back to the striker on the edge of the box, with Sears shot too powerful and accurate for the 'keeper as Hayden Mullins' side took a two-goal advantage.
It would remain at 2-0 to the U's until the break, but Shamal George had to be alert to collect a swerving cross from the right flank to prevent what would have been a late confidence boosting goal for Sudbury.
After half time, the U's kept pressing, but had to be aware of the threat from a rallied home side who were being roared on by their capacity crowd.
Dobra looked lively, and was an ever-present goal threat for Colchester United. His twists and turns proved difficult to control from the home defence, but he was unable to test the 'keeper.
He collected the ball from a recycled corner, and had an effort from a similar position to which he scored on Saturday, but lifted his looping effort just over the bar and into the Colchester United fans behind the goal.
Dobra was the provider for the third U's goal of the evening, playing a short corner to Sylvester Jasper. The on-loan forward looked up and spotted the 'keeper off his line, curling the ball over him and into the back of the net.
The U's professional performance carried on right until the final whistle, with just one real further chance for the home side, with Frimpong unmarked at the back post. His header went wide of George's goal though, and the U's kept a clean sheet.
Shawn McCoulsky netted the fourth goal in stoppage time with a well-taken volley from Luke Hannant's cross to cap a good performance from the U's as they ensured their name would be in the hat for the Second Round.
The draw for the next round of the Emirates FA Cup is on Monday night at around 10pm, where Hayden Mullins' will learn who his side will face at the start of December.
AFC Sudbury starting XI: Blunkell, Keys, Harris, Turner, Grimwood, O'Malley, Nyadzano, Frimpoong, Shaw (Gilchrist 78'), Temple (Clowsley 54'), Andrews (Hipkin 69').
Unused subs: Adams, Askew, Girling, Mayhew.
Colchester United starting XI: George, Clampin (Coxe 11'), Chambers, Wiredu, Skuse (Cooper 72'), Sears (McCoulsky 72'), Chilvers, Jasper, Eastman, Dobra (Nouble 72'), Tchamadeu.
Unused subs: Turner, Welch-Hayes, Smith, Hannant, Kennedy.