Posh are now 13 points adrift of safety with just 12 games remaining and their brief flirtation with second-tier football is rapidly coming to an end.
It was the home side's first game since allowing captain George Boyd to join Nottingham Forest this week, with goalkeeper Joe Lewis handed the skipper's armband in his absence.
Gannon had won both of his previous home games since replacing Mark Cooper last month but saw Chris Coleman's visitors edge a nervy game as they moved to within three points of the top six.
Winger Chris Whelpdale took just nine seconds to smash a shot inches wide from the edge of the area as Posh made a lively start, while Coventry goalkeeper Keiren Westwood had to be alert moments later to parry another smart shot from Whelpdale.
But Coleman's visitors grew in presence as the half wore on, with Northern Ireland international Sammy Clingan pulling the strings in midfield.
But there was no clever midfield play to be seen in Stead's 24th-minute opener.
Former Portsmouth defender Martin Cranie lumped a long ball forward and Stead gave chase.
He looked second favourite to win the ball but shrugged off the challenge of defender Craig Morgan and stabbed the ball past the onrushing Lewis.
Tommy Rowe saw a powerful drive blocked as the home side looked for an immediate response but Coventry easily saw out the rest of the first half.
Clingan was replaced at the break through injury before Posh defender Mark Little came close to a goal on his debut with a volley which was well blocked.
Coventry centre-half James McPake sent a decent header just wide from a free-kick as the Sky Blues looked for a killer second before Clinton Morrison saw an effort deflect narrowly wide.
Charlie Lee and Lee Frecklington both shot over as Gannon's charges mounted one final rally but Coventry held on to clinch a vital three points.
The Sky Blues have been languishing in the Championship for nine years but if they can maintain their current form they may have a chance of securing promotion, while Gannon must already be planning for a campaign in League One.