Hibs were the first to create an opening of note when Steven Fletcher picked out Jonatan Johansson at the near post, but his header rippled only the side of the net after seven minutes.
The home side, however, were showing more of an appetite for the game and they took the lead on 15 minutes.
Eric Odhiambo set up Dougie Imrie, who in turn found David Proctor in space and from 12 yards out he calmly slotted past Grzegorz Szamotulski.
Seven minutes later, a disjointed Hibs squandered a wonderful opportunity to level as Ross Chisholm's throughball found Johansson but, from the edge of the box, the Finnish striker rolled a weak effort wide of the post.
This was about the best the visitors could muster against a Caley Thistle side showing plenty of verve, despite at times lacking that little bit of quality in the final third.
In a two-minute spell before the interval, however, Inverness twice went close to scoring. Odhiambo was the provider both times, setting up Foran, who was only a whisker away from his first goal for the club on each occasion.
The second half started with little cohesion from either side, but Caley Thistle extended their lead on 65 minutes from a rare opportunity.
The hard-working Imrie was superbly denied from close range by Rob Jones only for the ball to break kindly for Foran who ensured that it was third time lucky with a powerful effort that gave Szamotulski no chance.
Hibs brought on Colin Nish and he came close to pulling one back, but Ryan Esson, in a rare moment of activity, was out quickly to snatch the ball off his toe and avert the danger.
It was about as close as the visitors came to scoring throughout the 90 minutes as Caley Thistle comfortably claimed a much-needed three points in their fight for SPL survival.