Portsmouth put their off-field troubles to one side as Joel Ward's effort sunk struggling Coventry to give Michael Appleton his first win at the helm.
The south coast club's owners, Convers Sport Initiatives, went into administration last week.
Greg Halford had broken the deadlock for the hosts from the penalty spot after Joe Murphy fouled Ward.
Lukas Jutkiewicz levelled from Richard Wood's cross, but Ward won it after being teed up by George Thorne.
Coventry are in deep trouble at the bottom of the table after losing five of the last six league games.
They fell behind in the 20th minute when Halford scored from the spot after a mix-up between Martin Cranie, Richard Wood and Joe Murphy which saw the latter trip Ward.
Portsmouth almost pressed the self-destruct button just before half-time as Halford conceded possession in his own half, allowing Jutkiewicz to break away - but his cut-back for Clive Platt was easily gathered by Stephen Henderson.
Coventry were not to be denied and Wood's superb left-wing cross was turned home by Jutkiewicz in the 54th minute.
But the Sky Blues were level for just five minutes before Thorne - who has followed Appleton from West Brom to the south coast - set up Ward to fire across goal and into the bottom corner from the edge of the box.
Henderson denied Gary McSheffrey as the visitors looked for an equaliser, but it is now 10 games without a win for Andy Thorn's side.