On-loan Tottenham winger Giovani Dos Santos and Spanish striker Pablo Counago netted for Town, while Clinton Morrison got a second-half consolation for the visitors, who battled away throughout.
Coventry made the brighter start with Robbie Simpson and Leon Best both shooting wide, either side of a Counago 20-yard curler which went just past the post.
Jon Stead converted a Counago pass but he was offside and Jaime Peters' cross was just too high for David Norris as Town upped the tempo.
They duly got the breakthrough on 24 minutes when Counago fed Dos Santos who cut in from the right wing and fired an angled drive beyond Keiren Westwood with the aid of a deflection.
On 26 minutes it was 2-0 when Kevin Lisbie crossed, Stead's shot on the turn struck Coventry defender James McPake in the face, but rebounded kindly to Counago, who cleverly clipped over Westwood.
Westwood denied Lisbie and Stead, while at the other end Peters and Alex Bruce made fine blocks to deny Eastwood and Doyle respectively, while Richard Wright saved a Best header.
Town should have scored a third on 52 minutes when Stead's cross found Norris six yards out, but his goalbound shot hit team-mate Counago, deflected onto the bar and was scrambled clear.
The game went into a flat period before livening up late on as first Stead found sub Danny Haynes but his chip over Westwood went wide.
Morrison then gave Coventry hope when he prodded home from close range on 79 minutes after Elliot Ward headed down an Eastwood corner.
Wright denied Morrison by racing out of his area and then he tipped over a deflected Eastwood shot, before the final kick of the match saw Simpson curl his free kick from 20 yards against the angle of post and bar with Wright well beaten.
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