Aaron's Doran's sixth-minute opener had the hosts in front at the interval, but Elliott levelled matters in the 54th minute to ensure Hearts made it eight games unbeaten against Caley Thistle.
Inverness defender Ross Tokely was given his marching orders for a second yellow card 12 minutes from time, but the home side comfortably held on to claim a deserved point.
Caley Thistle fielded the same starting line-up that drew 1-1 at Kilmarnock last weekend - a result that ended their top-six hopes. Manager Terry Butcher also named an unchanged bench with the only absentees the injured trio of Graeme Shinnie, David Proctor and Dani Sanchez.
Following their goalless draw at home to Motherwell seven days ago, Jambos boss Jim Jefferies made two changes, bringing in Suso Santana and Andrew Driver. Out went David Templeton and Jason Thomson, while Marius Zaliukas took a place on the bench.
Looking to end the season on a high, Inverness started at a strong pace and Richie Foran outmuscled Andy Webster before sending in a cross that Adam Rooney was only inches away from converting.
Hearts failed to heed the early warning and fell behind with only six minutes gone.
Rooney was sent charging away down the left by Lee Cox and his delivery to the back post was calmly despatched by the unmarked Doran for his second goal since joining in January on loan from Blackburn.
The visitors' response was slow in coming, but then Suso sent in a low effort that was easily held by Ryan Esson.
It was Caley Thistle, however, who were continuing to create the better chances, Rooney's header from a Cox cross well saved by Jamie MacDonald at his near post.
The game then drifted into a lull, but Inverness remained the team offering the more potent threat while Hearts showed little evidence they could trouble the hosts' defence.
Foran was at the heart of everything for Caley Thistle and his low cross found Nick Ross, who in turn set up Rooney, but he tried to place the ball past MacDonald from an angle only for the goalkeeper to parry it away.
Rooney was then unfortunate moments later as MacDonald got his outstretched boot to turn away the shot after good work by Doran.
Suso was proving to be the most lively attacking player for Hearts and his cross was almost headed home by Driver, but Esson got across his goal smartly to make the save.
It sparked a more promising spell for Hearts before the break and only a wonderful clearance on the line by Stuart Duff prevented Rudi Skacel's close-range effort from restoring parity.
Inverness were then fortunate to escape again at the start of the second half. This time Ryan Stevenson's header was touched goalwards by Elliott, but Rooney was well positioned to scramble the ball to safety.
It was Hearts doing all the attacking and they made the pressure pay in the 54th minute.
Suso drove into the Caley Thistle box and his cut-back found the unmarked Elliott, who from eight yards slid the ball into the corner of the net with a delightful finish past the exposed Esson.
A mistake by Kenny Gillet then presented Suso with the chance to head towards goal again and he picked out Stevenson, but this time Esson was equal to the effort, making a fine save down to his right.
Caley Thistle also had an attempt of their own cleared off the line.
Cox sent in a cross to the back post that was headed across goal by Foran. It seemed a formality that Rooney would add the finishing touch, but Webster got his foot to the ball to make the clearance from underneath his own bar.
Tokely then turned from saint to sinner in the latter stages. First he got in the way of Stevenson's goalbound effort, only to be shown a second yellow card moments later for hauling down Hearts substitute David Templeton.
This forced Caley Thistle into a defensive reshuffle with Grant Munro replacing Doran as Inverness attempted to see out the remainder of the game with 10 men.
Despite their numerical advantage, Hearts failed to make it count as both sides had to settle for consecutive draws in the SPL.