Match ends, Hearts 2, Hibernian 0.
Hearts staved off relegation until Wednesday at least by consigning Edinburgh rivals Hibernian to a third straight defeat.
Dale Carrick's emphatic finish from close range gave the hosts an early advantage.
Jordon Forster had a goal wrongly disallowed for offside on a frustrating day for the visitors.
Hibs had Alan Maybury sent off before substitute Billy King rounded Ben Williams to score Hearts' late second.
Victory buoys bottom club Hearts but demotion from the Scottish Premiership will be confirmed for Gary Locke's side if they lose to Aberdeen in midweek.
For Hibs, their ninth loss since Terry Butcher took charge in November leaves them six points above the relegation play-off spot.
The early tension at Tynecastle was illustrated by a high challenge by Lewis Stevenson in which the Hibs player's studs caught the chest of Callum Paterson.
However, Paterson showed no signs of injury when he played a major role in the opening goal as the visitors' recent defensive frailties were laid bare.
His cross from the right was deftly headed down by Ryan Stevenson for Carrick, who kept his cool in controlling the ball before lashing past Ben Williams.
Hibs, showing six changes from last week's defeat by St Johnstone, were rocked by the early set-back but gradually worked their way back into the game.
Danny Handling found space on the edge of the Hearts area, but his shot was too high.
And Sam Stanton pulled a free-kick wide, much to the delight of the home fans now revelling in the atmosphere.
There were more ironic cheers from the Hearts fans when James Collins sent a shot skywards following some superb set-up play by Duncan Watmore.
Hearts knew a second goal would further sink Hibs' fragile confidence and Sam Nicholson, who earlier netted after a dubious offside flag had been raised against a team-mate, tested Williams with a powerful diagonal shot.
David Smith also came close for the home side in the early moments of the second half, driving narrowly wide after being released by the industrious Carrick.
Hibernian's claims of handball against Dylan McGowan fell on deaf ears after the defender had blocked Collins' shot on the edge of the box.
Ryan McGivern was off target with two efforts at the Hearts end before the game's most controversial moment.
Forster rose to head in a deep Stevenson cross but his celebrations were cut short by the the offside flag. However, television replays revealed the Hibs man had in fact been played onside by McGowan.
And Hibs' day went from bad to worse when Maybury received a second yellow card for tripping King as Hearts mounted a counter attack.
Another breakaway was the catalyst for Hearts' clincher as King was sent clean through on goal by Stevenson and the youngster kept his footing after evading Williams to net his first goal for the club.
- 17SmithSubstituted forMcCallumat 77'minutes
- 15HoltSubstituted forRobinsonat 87'minutes
- 18CarrickSubstituted forKingat 83'minutes
- 7StevensonBooked at 28mins
- 18MayburyBooked at 90mins
- 3McGivernBooked at 61mins
- 20TaiwoSubstituted forThomsonat 70'minutes
- 22WatmoreSubstituted forHarrisat 68'minutes
- 19HandlingSubstituted forCairneyat 85'minutes
- Steven McLean
- Shots on Target
Second Half ends, Hearts 2, Hibernian 0.
Corner, Hearts. Conceded by Michael Nelson.
Scott Robinson (Hearts) wins a free kick in the attacking half.
Foul by Paul Cairney (Hibernian).
Goal! Hearts 2, Hibernian 0. Billy King (Hearts) left footed shot from the centre of the box to the centre of the goal. Assisted by Ryan Stevenson.
Second yellow card to Alan Maybury (Hibernian).
Billy King (Hearts) wins a free kick in the defensive half.
Foul by Alan Maybury (Hibernian).
Foul by Dylan McGowan (Hearts).
Samuel Stanton (Hibernian) wins a free kick in the defensive half.
Substitution, Hearts. Scott Robinson replaces Jason Holt.
Attempt missed. Samuel Stanton (Hibernian) left footed shot from outside the box is too high from a direct free kick.
Substitution, Hibernian. Paul Cairney replaces Daniel Handling.
Foul by Ryan Stevenson (Hearts).
Kevin Thomson (Hibernian) wins a free kick in the defensive half.
Substitution, Hearts. Billy King replaces Dale Carrick.
Corner, Hibernian. Conceded by Callum Paterson.
Corner, Hibernian. Conceded by Dale Carrick.
Attempt missed. Danny Wilson (Hearts) header from the left side of the box is high and wide to the left.