Second-half goals from Ross Draper and Andrew Shinnie, either side of Leigh Griffiths' 23rd goal of the season, were enough to earn them the victory, keeping them three points behind Motherwell in second and extending their lead over Ross County in fourth to five points.
For Hibernian the result spoiled the return to the club of Scotland international Kevin Thomson and leaves the club languishing in eighth place, having won only one of their last nine league games at Easter Road.
Hibs set themselves out in an attack-minded 4-3-3 with Griffiths, on the right of the front three, under no obligation to track the advancing full-back. To balance against defensive vulnerability they would shift into a more balanced 4-4-2 when their opponents were in possession.
Terry Butcher would not have been content with the way in which his team had yielded the advantage to Hibs after the first 15 minutes. Demonstrating their desire to win the match they pushed much further forward as a team in the second half and found their reward after only four minutes.
Graeme Shinnie's long ball through the centre found the run of Draper, who had drifted in from the right. The midfielder kept his cool to delicately lob the ball over the reach of the stranded Ben Williams and into the back of the net.
Not content with a single goal, Inverness continued with their attacking ethos but it almost cost them the lead within six minutes of taking it. On the counter-attack, Doyle skipped past Daniel Devine before squaring to a completely free Griffiths, who struggled to get the ball out from under his feet prior to seeing his shot saved by the advancing Reguero.
The chance reignited a sluggish Hibs and they were on level terms five minutes later. Gary Deegan's shot from 25 yards had power but would have lacked the direction to beat the keeper had it not been for the ricochet the ball took off Griffiths' calf, which sent the ball spinning into the corner of the net.
Inverness were vehement in their claims that Griffiths had been in an offside position, but their grumblings were soon forgotten when they retook the lead. Again a deflection played a huge part in the goal, with Andrew Shinnie's shot from the edge of the penalty area beating Williams after striking Hibs captain James McPake.
Hibs boss Pat Fenlon threw on Paul Cairney and Scott Robertson with a view to his side hauling themselves back into the game but it was Billy McKay who almost grabbed the game's next goal 10 minutes from time. The diminutive striker was sent through before a last-ditch challenge from McPake blocked his shot inside the penalty area.