David Raven, Marley Watkins, Billy McKay and Greg Tansey all saw efforts either strike the post or crossbar, while Jamie Hamill passed up Hearts' best chance late in the second half.
Inverness boss Hughes named the same starting line-up that had drawn 2-2 at Stranraer in the fifth round of the Scottish Cup last weekend.
Richie Foran, still making his way back to full fitness from ligament damage to his shoulder, was again amongst the substitutes for Caley Thistle.
Hearts, who have not played since losing to Inverness in a penalty shootout in the semi-finals of the Scottish League Cup at the start of the month, gave a first start to on-loan West Ham United striker Paul McCallum.
David Smith was missing with a fractured knee, while suspensions ruled out both Kevin McHattie and Callum Paterson, but there was a return for Jason Holt, who was named on a Hearts bench that only included five players.
Caley Thistle were given a pre-match boost with the announcement that midfielder James Vincent, out of contract at the end of the season, had signed a new deal with the club until May 2016.
It was Hearts, however, who made the brighter start with Ryan Stevenson seeing his dipping effort from 25 yards touched over by Dean Brill.
Play quickly switched to the other end and Marley Watkins cut in from the right before drilling a low shot from the edge of the 18-yard box narrowly wide.
Caley Thistle were beginning to assert themselves on proceedings and only a timely block by Danny Wilson in front of goal foiled McKay from turning home Graeme Shinnie's cross after Raven's attempted cross had come off the face of the bar.
Gary Warren then headed a Shinnie corner over before Tansey tried his luck with the head as well, only to see Jamie MacDonald in the Hearts goal make a decent save following good work out wide by Watkins.
Watkins was causing all sorts of problems for the visitors and his through pass gave McKay a sight of goal, but from a tight angle his effort was blocked by MacDonald.
The pair then swapped roles moments later, Watkins this time going clear from McKay's pass and although his effort beat MacDonald, Jordan McGhee had got back to make a spectacular clearance off the line.
Hearts were being overwhelmed and only the woodwork denied Watkins and then McKay in quick succession as Caley continued to push for the breakthrough.
Somehow, Hearts made it to the interval unscathed, although not without one further scare, Tansey this time thumping the ball off the post to end a first half that was dominated by the hosts.
The Jambos arrived in the Highland capital on the back of a three-game unbeaten run in the league and they almost scored against the run of play early in the second half, a piledriver from 25 yards by Hamill just flying wide.
Stevenson then tested the reflexes of Brill from 18 yards, but the home goalkeeper stood firm to punch the shot away.
It was only brief respite for Hearts, however, as MacDonald had to scramble across to turn away Tansey's 20-yard drive for a corner.
As the game entered the latter stages, Hamill had a wonderful chance to open the scoring, but from 16 yards out and with no one around him he fired his shot high over the bar.
As Inverness pressed for a winner, McCallum could have stolen the points with a late header, but Shinnie was on hand to clear away the danger.