The striker put Billy Davies' side on their way to three points with a precise finish just before half-time, before Dexter Blackstock smashed home a second 12 minutes from the end to kill off the Sky Blues' resistance.
It was Forest seventh win in their last eight matches at the City Ground, where they have now scored 14 goals in their last four outings.
Forest had made a lively start, with Davies making five changes to field a highly attacking line-up, but it was actually Coventry that spurned the first real opportunity of the game when Leon Barnett sent a close-range header over the bar.
Nathan Tyson had seen an early strike ruled out for offside, after he had sent a rifling shot into the net off the underside of the bar.
Kelvin Wilson shook off an early knock to send a powerful header narrowly wide of the post after Nicky Shorey had delivered a precise cross towards the near post.
And Earnshaw thought he had scored when he sent a rising shot goalwards, only for Keiren Westwood to produce a spectacular save, stretching out full length to palm over.
Forest were generally in charge, although the Sky Blues continued to carve out chances of their own, with a rare misjudgement by Lee Camp almost costing the home side dear, as he stooped to collect a skimming 25-yard shot from Leon Best, only to see the ball bounce of his shoulder and just wide of the post.
A bending shot from skipper Paul McKenna offered a reminder of Forest's threat, before they eventually took the lead through an outstanding quick break.
Radoslaw Majewski had plenty of work to do as he carried the ball into the Coventry half with only three opposition defenders for company, but a surging run through the centre from Tyson attracted the attention of two of them, allowing the Pole to slide an inch-perfect pass into the path of Earnshaw, who lifted a composed finish over the advancing keeper in the 42nd minute.
Camp was back to his best after the break making a smart early save to thwart Clinton Morrison, after he had produced a neat shot on the turn.
But Forest twice threatened themselves, with Blackstock just failing to connect with a smart cut-back from Tyson, before returning the favour by sending Tyson through on goal, only for striker to shoot wildly with his weaker right foot.
And, when substitute Dele Adebola used his strength to turn on the byline on the left side, it set up Blackstock to smash an emphatic finish high into the corner of the net to make sure of the points.
Adebola himself could have added a third, but was just off-target after bursting through the centre.