Hearts hit back twice to earn a point at home to 10-man Ross County.
Graham Carey intercepted a pass from Callum Tapping to run in and shoot County in front on 20 minutes but Callum Paterson levelled soon after.
Melvin De Leeuw drove the visitors ahead after the interval before Richard Brittain picked up his second caution.
With Hearts piling forward, Ryan Stevenson bundled the ball over the line from a corner, with Paterson hitting the crossbar late on.
Every point is crucial for Hearts as they gradually near positive figures following their 15-point deduction for entering administration.
They are now on -3 but made up small ground on 11th-place Kilmarnock, who lost at home to Motherwell.
Derek Adams' men came agonisingly close to a first league win since 5 October.
Both sides had early opportunities to take the lead. Kevin Luckassen found space inside Hearts 18-yard box but his curling shot was wide of Jamie MacDonald's goal.
At the other end good play by Paterson down the left set up Scott Robinson for a deep cross that Jamie Walker was inches away from connecting with.
Hearts always looked dangerous going forward and a mix up in the County defence almost led to the opening goal.
Centre half Scott Boyd collided with keeper Mark Brown as a cross came into the box and neither knew where the ball was before it hit the shin of Boyd and slowly rolled wide.
Walker had a crack at goal but midway through the first half a terrible mistake by Tapping allowed Ross County to take the lead.
The youngster tried an ambitious pass across the field that was intercepted by Carey, who found himself clean through on goal and fired the ball underneath the body of MacDonald.
Their lead lasted just six minutes, though.
Robinson mis-hit a corner but the ball eventually found its way to Paterson who fired an unstoppable left foot volley beyond Brown and into the net.
Brittain found his way into the book of referee Crawford Allan after wrestling Walker to the ground.
De Leeuw rattled the underside of the bar but County regained the lead when Hearts failed to clear the ball and De Leeuw fired the ball low into the corner.
Brittain fouled Walker again to collect his second booking.
Hearts pressed again and substitute David Smith shot over from close range before 'keeper Mark Brown held on to Stevenson's effort from 20-yards.
Their numerical advantage was eventually made to count two minutes from time when Stevenson bundled the ball home from a corner.
Smith's delivery was knocked down by Danny Wilson and the forward forced the ball home inside a congested six-yard box.
Paterson crashed a header off the bar from a Smith free kick as the Jambos nearly took all three points.
Heart of Midlothian
- 01 MacDonald
- 30 McGhee
- 03 McHattie
- 20 Tapping (Smith - 57' )
- 05 McGowan
- 04 Wilson
- 02 Hamill
- 08 Robinson (King - 80' )
- 12 Paterson
- 07 Stevenson
- 14 Walker
- 13 Ridgers
- 16 McKay
- 17 Smith
- 18 Carrick
- 19 King
- 26 King
- 29 Oliver
- 01 Brown Booked
- 04 Kettlewell Booked
- 11 De Leeuw (Maatsen - 78' )
- 06 Micic
- 21 McLean
- 05 Boyd
- 08 Brittain Dismissed after an earlier booking
- 10 Quinn
- 15 Glen (Klok - 70' Booked )
- 19 Luckassen
- 23 Carey Booked
- 02 Kovacevic
- 09 Mustafi
- 14 Maatsen
- 16 Cooper
- 17 Ross
- 18 Klok
- 20 Fraser
Ref: Crawford Allan