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Evans went close for Chesterfield early on before the visitors went ahead midway through the first half when Jay O'Shea calmly slotted in from close range from Kristian Dennis' threaded pass.
Sam Walker pushed away O'Shea's low effort soon after, but Kurtis Guthrie's diving header flashed inches wide and Drey Wright was denied by keeper Ryan Fulton.
Colchester needed just 53 seconds to equalise after the interval when substitute Tarique Fosu netted with his first touch after coming on with a low finish, after the ball had broken to him in the area.
Colchester captain Luke Prosser's header from Wright's corner then rattled the bar.
But Chesterfield restored their advantage six minutes into the second half through Evans, who emphatically volleyed home after Tom Anderson had nodded on a free-kick in the area.
Guthrie was later denied by Fulton but Chesterfield claimed a narrow victory.
Report supplied by the Press Association.
Match ends, Colchester United 1, Chesterfield 2.
Second Half ends, Colchester United 1, Chesterfield 2.
Richard Brindley (Colchester United) wins a free kick on the left wing.
Foul by Jay O'Shea (Chesterfield).
Foul by Richard Brindley (Colchester United).
Ched Evans (Chesterfield) wins a free kick in the attacking half.
Attempt saved. Macauley Bonne (Colchester United) header from the centre of the box is saved in the top right corner.
Luke Prosser (Colchester United) wins a free kick on the right wing.
Foul by Ched Evans (Chesterfield).
Ched Evans (Chesterfield) wins a free kick in the defensive half.
Foul by Denny Johnstone (Colchester United).
Substitution, Colchester United. Louis Dunne replaces Alex Wynter.
Macauley Bonne (Colchester United) wins a free kick in the defensive half.
Foul by Connor Dimaio (Chesterfield).
Attempt saved. Macauley Bonne (Colchester United) right footed shot from the left side of the box is saved in the bottom right corner.
Foul by Kurtis Guthrie (Colchester United).
Gboly Ariyibi (Chesterfield) wins a free kick in the attacking half.
Luke Prosser (Colchester United) wins a free kick in the attacking half.
Foul by Tom Anderson (Chesterfield).
Corner,  Chesterfield. Conceded by Alex Wynter.
Substitution, Chesterfield. Liam Graham replaces Kristian Dennis.
Substitution, Colchester United. Macauley Bonne replaces Sammie Szmodics.
Foul by Gary Liddle (Chesterfield).
Tarique Fosu-Henry (Colchester United) wins a free kick on the left wing.
Dion Donohue (Chesterfield) wins a free kick on the right wing.
Kurtis Guthrie (Colchester United) is shown the yellow card for a bad foul.
Foul by Kurtis Guthrie (Colchester United).
Attempt blocked. Craig Slater (Colchester United) right footed shot from outside the box is blocked.
Foul by Connor Dimaio (Chesterfield).
Richard Brindley (Colchester United) wins a free kick in the defensive half.
Foul by Gary Liddle (Chesterfield).
Tarique Fosu-Henry (Colchester United) wins a free kick in the defensive half.
Delay in match Ched Evans (Chesterfield) because of an injury.
Ched Evans (Chesterfield) wins a free kick in the defensive half.
Foul by Alex Wynter (Colchester United).
Substitution, Chesterfield. Jon Nolan replaces Liam O'Neil because of an injury.
Attempt missed. Kristian Dennis (Chesterfield) right footed shot from outside the box is close, but misses to the left.
Attempt blocked. Kristian Dennis (Chesterfield) right footed shot from outside the box is blocked.
Attempt saved. Kurtis Guthrie (Colchester United) right footed shot from the left side of the box is saved in the centre of the goal.
Gboly Ariyibi (Chesterfield) wins a free kick in the attacking half.
Ched Evans grabbed the winner as Chesterfield ended their long run without a victory by triumphing at Colchester United in the FA Cup first round.