Hearts secured European football next season with a point but missed the chance to narrow the gap to second-placed Aberdeen to six points.
Neither side were potent offensively in a largely dull contest with chances and attempts on goal very rare.
Substitute Abiola Dauda almost notched a late winner as Hearts began to press.
But, as the angle narrowed, Inverness Caledonian Thistle goalkeeper Owain Fon Williams managed to stop his flick towards the far corner.
Danny Williams had a late strike well saved and Josh Meekings and Liam Polworth came close for Caley Thistle with shots narrowly over the bar, but neither side really did enough to merit victory.
Hearts’ motivation was to give themselves a realistic chance of catching Aberdeen.
To do that, a win seemed vital, but there was little sign of it arriving, although this point guarantees them a Europa League qualifying spot for next season.
Caley Thistle could have moved into seventh place and ended any real concern of being in the relegation play-off position.
The first real moment of interest was when Miguel Pallardo was caught heavily by Ross Draper after the Inverness midfielder had taken a heavy touch.
Referee Don Robertson waved play on, but Hearts head coach Robbie Neilson was infuriated on the touchline.
The midfielder soldiered on but was eventually replaced with Callum Paterson, who had returned from injury to take his place on the bench.
It was lacking any invention or excitement but livened up when Jamie Walker went down under Carl Tremarco’s challenge.
Referee Don Robertson booked the Hearts man for diving, again to the fury of Neilson.
Caley Thistle’s Liam Polworth almost created an opening with a great first touch, but he went too close to the by-line and no-one broke into the box to get on the end of his chip across goal.
Hearts’ Juwon Oshaniwa had a powerful drive blocked before Caley Thistle’s Josh Meekings and Polworth sent drives flying narrowly over.
However, the threat was minimal at best overall and the second half followed a similar pattern.
Dauda had a great chance on the edge of box but blazed high over when composure may have paid off.
The striker then got a clear sight of goal in the inside left channel, but the onrushing Fon Williams did well to narrow the angle and block when a goal looked likely.
Iain Vigurs tried to add to his recent goal spree with a driven ball across the six-yard box, but Neil Alexander comfortably held on before he did so again from a Danny Williams volley as the match ended in stalemate.