The Sky Blues could have gone in front early on at the Ricoh Arena through defender William Edjenguele and then David McGoldrick, who had an eighth-minute effort ruled out.
But the home side only had to wait three more minutes before they took the lead. McGoldrick, on loan from Nottingham Forest, won a header three yards outside the area, brought the ball down well and curled home a right-footed effort past Chris Day.
That appeared to wake Stevenage and they began to get a foothold in the game. Robin Shroot turned that into something tangible in the 21st minute. The visitors broke impressively and when Luke Freeman's shot was parried by Joe Murphy, Shroot followed up to convert.
Coventry had further cause for complaint in the 27th minute when Stephen Elliott netted but was harshly judged to have been offside.
Neither side grabbed the game by the scruff of the neck at the start of the second half, but Stevenage made three changes and they paid dividends when Marcus Haber headed powerfully home in the 71st minute - sealing a third successive away win.