Inverness midfielder John Rankin scored against Falkirk for the fourth time this season to deny the Bairns a third successive victory in the Bank of Scotland Premier League.
Falkirk looked to have pinched the points when substitute Carl Finnigan lashed home the game's opening goal in the 80th minute.
But six minutes later Rankin struck again to continue his remarkable scoring record against the Bairns.
He netted twice when the teams meet at the Tulloch Stadium earlier in the campaign, when Inverness won 3-2, and then hit the reply when Falkirk won 3-1 at their home on December 30.
The late leveller came as a relief to Inverness, who were without their suspended captain Darren Dods and banned midfielder Ian Black.
Stuart McCaffrey joined Grant Munro in the centre of defence, while Roy McBain was on the bench after recovering from a groin injury. Barry Wilson returned in midfield, with Markus Paatelainen relegated to substitute.
Falkirk manager John Hughes named an unchanged line-up after successive wins over Celtic and St Mirren.
Striker Finnigan was named on the bench on his return from suspension but would play an important role late in the game.
Craig Dargo forced Kasper Schmeichel into a superb sprawling early save as Inverness carved out the first opportunity, and Wilson then sent the ball wide.
Seventh-placed Falkirk and Inverness - who climbed a place to ninth with their point - had played three times previously this season, including a CIS Insurance Cup tie, and will meet again following the split.
Falkirk's six goals in those fixtures all came from Anthony Stokes, now at Sunderland, so they needed to find a threat from elsewhere.
Defender Dean Holden headed wide from close range as the visitors threatened early on.
At the other end another Wilson effort from the edge of the penalty area forced Schmeichel to make a save, and the Dane produced another fine stop soon afterwards when Richie Hart unleashed a classy volley from 20 yards.
As the midway point of the first half arrived, Wilson tried his luck again but his shot went wide of the busy Schmeichel's goal.
Inverness were on top but Falkirk still carried a threat.
Stephen O'Donnell headed over from a half chance, and his midfield colleague Patrick Cregg was off target from another opportunity after a decent approach.
Rankin then almost netted when his stunning left-footed attempt swerved and only just missed the top right corner with Schmeichel apparently beaten.
Falkirk substituted Holden early in the second half, the former Peterborough full-back struggling with a leg muscle injury as Thomas Scobbie took his place.
Their set-pieces, from Russell Latapy, were a feature of the early stages of the second period. But Latapy's two corners and one free-kick from a dangerous position in the first 10 minutes did not carry quite the threat the veteran Bairns midfielder would have hoped for.
Falkirk offered little menace in open play, with Pedro Moutinho and Alan Gow not linking up in attack as well as Hughes would have hoped.
Falkirk defender Kenny Milne went into the book for a reckless foul on Hart, but Inverness failed to make the most of the free-kick from Rankin which followed.
Wilson was replaced by McBain in the 66th minute as Inverness made their first change.
Falkirk made their second substitution shortly afterwards when Finnigan entered the action and Moutinho made way. It livened up the match.
Inverness goalkeeper Michael Fraser gathered the ball well from the feet of Rangers-bound Gow as Falkirk looked for the breakthrough goal.
The impressive Schmeichel continued to keep out Caley Thistle, handling well from a free-kick.
Falkirk made a third change with Latapy being allowed a rest, as Liam Craig came on.
Inverness made their protests known to referee Crawford Allan when Finnigan was flagged offside following a pass from Gow.
But soon Finnigan and Falkirk were celebrating as the former Newcastle reserve thrashed a fine shot past Fraser after escaping his marker, giving the visitors the lead with 10 minutes remaining.
Caley boss Charlie Christie sent on Rory McAllister for Russell Duncan shortly afterwards, and it was not long before the home side were level.
Rankin was predictably the scorer from close range in the 86th minute, and the goal revived the home side's interest in winning the match.
Dargo burst past Schmeichel and looked set to slot home a late clinching goal, but Falkirk's defence got back well to clear the danger and secure a point.
Teams:
Inverness CT Fraser, Tokely, McCaffrey, Munro, Hastings,Wilson (McBain 66), Hart, Duncan (McAllister 82), Rankin,Bayne, Dargo.
Subs Not Used: Ridgers, Paatelainen, Wood, Soane, Sutherland.
Booked: Tokely.
Goals: Rankin 86.
Falkirk Schmeichel, Ross, Barr, Milne, Holden (Scobbie 48),Cregg, Latapy (Craig 75), Thomson, O'Donnell,Moutinho (Finnigan 68), Gow.
Subs Not Used: Lambers, Uras, Mcstay, Lima.
Booked: Milne.
Goals: Finnigan 80.
Att: 4,435
Ref: C Allan (Scotland).