Ellington combined with Jason Roberts and the unmarked Gary Teale charge onto the ball before cracking a low drive past Ian Bennett for the opener.
Matt Jackson fouled Gary McSheffrey in the box and he got up to score from the spot to level for the home side.
Coventry were denied by a combination of the woodwork and the outstanding John Filan before Ellington's volley from 25 yards secured the three points.
Wigan boss Paul Jewell said:
"It was all about fight and determination and getting the three points.
"I said to the players 'We are playing for big stakes here'. I said:
'Remember how it felt last year'."
Coventry: Bennett, Williams, Shaw (Jorgensen 20), Hall, Duffy, Doyle, Osbourne (Hughes 74), McSheffrey, Giddings (Whing 44), Benjamin, John.
Subs Not Used: Adebola, Barrett.
Booked: Doyle.
Goals: McSheffrey 22 pen.
Wigan: Filan, Eaden (Wright 79), Jackson, Breckin, Baines, Teale, Bullard, Whalley (Jarrett 76), McCulloch, Ellington, Roberts (Graham 86).
Subs Not Used: Walsh, McMillan.
Booked: McCulloch, Jarrett.
Goals: Teale 9, Ellington 68.
Att: 12,130.
Ref: R Beeby (Northamptonshire).