The Irish midfielder fired home the opener in the first half before hitting a scorching second after the break, after Andrew Whing's first league goal had given Coventry hope.
David Johnson made the points safe for Forest with a clinical finish midway through the second period.
Coventry almost made a dream start when Darren Ward nearly carried Youssef Safri's long-range shot over his own goal line after just 30 seconds.
Graham Barrett went close for the home side in the sixth minute but, after cutting inside Belgian full-back Davy Oyen, he fired wide from the corner of the box.
The visitors felt they should have had a penalty during a lively opening when Marlon Harewood went down under a challenge from Whing, but referee Paul Danson waved away their claims.
Paul Hart's side took the lead after 18 minutes when Harewood was given time and space to pick out Reid in the box. The young Irishman turned past Stephen Warnock before sliding home past Scott Shearer in the Coventry goal.
Reid had a golden opportunity to put Nottingham Forest 2-0 up but he glanced Harewood's right-wing cross wide when he should have scored.
Michael Dawson was guilty of the same error just before the break when he powered Stephen McPhail's corner wide of the post.
The Sky Blues began the second half on the front foot and equalised immediately. Whing latched onto a loose ball in the area before turning and hitting a low shot past Ward.
The teenage defender blotted his copybook, however, when he was booked for celebrating his goal by running to the home supporters.
City were dominant at the beginning of the second period, with Andy Morrell, Dele Adebola and Patrick Suffo all wasting great chances to hand the home side the lead.
Forest made Coventry pay in the 61st minute when Reid crashed home his second. McPhail's shot was blocked by Mo Konjic on the edge of the area but Reid followed up with a thunderous 25-yard effort which flew past Shearer and into the top corner.
Johnson could have made it three just seconds later but he fired over the bar from two yards.
The striker made up for that miss in the 66th minute when he latched onto Danny Sonner's pass and was given the freedom to run into the Coventry box before slotting past Shearer.
Keith O'Neill, who had not played for Coventry since December 2001 due to a catalogue of injuries, made a brief appearance as a substitute but only lasted eight minutes as he aggravated his hamstring.