Hearts' off-field problems are well-documented, with owner Vladimir Romanov voicing his desire to sell, £35million of debt and players going unpaid for a second successive month.
It may be coincidental, but since the first delayed payment of their wages this season, they had failed to score and collected one point from a possible 12 - before Saturday.
Rudi Skacel netted in the opening minute of the second half, but the lead did not last long as Ross Tokely equalised with a 58th-minute header.
However, Hearts responded and Eggert Jonsson netted a 75th-minute header to end a four-match winless run dating back to the October 15 win at Dunfermline.
Romanov this week suggested the club was worth £50m, but the only Hearts player to show significant value was Marian Kello.
The goalkeeper saved well from Gregory Tade and Andrew Shinnie as Caley Thistle were unable to claim a first win in Gorgie in four years.
Inverness named an unchanged side after Greg Tansey's red card against Celtic was rescinded by the Scottish Football Association on Thursday.
Hearts manager Paulo Sergio watched from the stand for the first time at Tynecastle, with the Portuguese serving the second of a five-match touchline ban after his dismissal in the loss to Kilmarnock earlier this month.
Blustery conditions contributed to a stop-start contest, with Jonsson and Tokely booked early on, before the hosts had the first opportunity.
Ryan McGowan stole the ball at the byline from a hesitant Jonny Hayes and cut it back, with David Templeton leaving it for Ryan Stevenson, who scuffed his shot straight at Ryan Esson in the Inverness goal.
Shinnie responded with a snap-shot from 25 yards which went narrowly wide before Kello's goal came under further pressure when a casual Marius Zaliukas failed to control a simple pass in defence.
Hayes stole in and played Tade through one-on-one, but the Hearts goalkeeper saved well with his feet.
Stevenson had another effort from the edge of the area before an incident which provoked Inverness' ire.
Templeton went down under in the box following an aerial challenge by Josh Meekings, who won the ball fairly.
From the subsequent drop ball, Stevenson played it through for Templeton who prodded straight at Esson.
Stevenson was then confronted by captain Richie Foran and Tokely and was withdrawn at half-time for Adrian Mrowiec.
Mrowiec's first act was to celebrate Hearts' first goal since mid-October.
It came 25 seconds after the restart when Skacel latched onto a ball down the right and hit an angled shot beyond Easson into the bottom corner.
It was Skacel's fourth of the season and he was booked for celebrating.
Shinnie shot over soon after, before Tokely equalised.
Hayes' free-kick from deep on the right evaded a static Hearts defence and the defender headed in at the back post.
Tansey blasted over from 30 yards after winning the ball well in midfield and an energised Inverness applied pressure on Hearts' defence again.
Tade robbed Andy Webster, Shinnie's effort was saved by Kello and Hayes hit the follow up over the bar.
Sutton's shot was deflected wide after he turned Chris Hogg and from the resulting corner the lead was restored.
A short corner was played, Templeton fired a cross inside the six-yard box and the ball ricocheted off Jonsson's head and in.
Sutton was replaced by Mehdi Taouil before Templeton hit a bouncing ball narrowly wide from a throw-in towards the edge of the box.
Tokely headed another Hayes free-kick wide when he could have done better as Inverness suffered a second straight loss.