Steven Pressley's side started the season on minus 10 points following administration, but Wilson's double ensured the Midlands club wiped out the deficit with six games gone.
Coventry are now on one point, although again the focus will be on the fact that the club's fans protested about playing home games at Northampton Town's Sixfields stadium by staying away.
A crowd of just 1,789 witnessed Coventry's victory, which is believed to be the club's lowest attendance for a home league game.
Leon Clarke was twice denied by the woodwork before Wilson found the net for the third League One game in a row after 38 minutes when he followed in Blair Adams' saved shot and tapped in from close range.
Wilson added his second just before the hour mark as he skipped past Colchester goalkeeper Sam Walker following good link-up play with Clarke.
Defeat signalled Colchester's first away league defeat of the campaign, with Wilson now having scored eight goals in six League One fixtures this season.
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