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Kenneth Vargas' first goal for Hearts delivered a much-needed Scottish Premiership victory for Steven Naismith's "controlled and patient" side, as they eventually broke down a stubborn Livingston.
The hosts were dominant, peppering the Livingston box with waves of attack, but a frustrating stalemate looked likely until Costa Rica international Vargas netted.
A neat pass from Jorge Grant, which wiped out the Livingston defence, was met and smashed into the roof of the net from close range by the substitute.
The win is Hearts' first in four, and will ease pressure on Naismith as his side shoot up to fourth.
"There was a real control about the performance," the Hearts head coach told BBC Scotland.
"If you are going to be a Hearts player, you need to have that calmness because as soon as you become more desperate, you lose the quality of chances. We created good chances, but it was about control and patience."
Livingston, who did not register a shot on target, remain in 10th.
Steven Naismith demanded a fast start from his much-changed Hearts side. He got it, but there was just nothing to show for it.
Lawrence Shankland left the crossbar shaking with a vicious strike, before forcing a strong save from the palms of a busy Jack Hamilton.
Livingston made a handful - if that - of visits if that into the Hearts half before the interval.
On one such occasion, Joel Nouble was tugged by the diminutive Cammy Devlin in a mismatched tussle. The home midfielder was cautioned and replaced off at the break.
The frustration lasted long into the night - until the 79th minute, to be precise - but lovely work from Grant meant Vargas had a simple task to net his first goal in front of a relieved Tynecastle crowd.
Nine shots, three on target, 20 touches in the Livingston box - the Scotland international was a menace all night. All he was missing was his goal.
This might have been one of the most dominant 1-0 affairs to be played in recent times.
Hearts recorded 25 shots to Livingston's three, with 10 on target to the visitors zero. Scintillating supremacy. But, when it comes to the one stat that matters, it's all too close for comfort.
Until Vargas' strike, it was missed opportunity after missed opportunity. However, the deserved goal was found, and Hearts can head into their League Cup semi-final with Rangers with a bit of confidence in the ranks.
For Livingston, though, it was another performance lacking anything resembling a threat in attack. It was 11 men behind the ball at all times and made for some very bleak viewing.
Martindale was unhappy with his side's defending against Dundee at the weekend and, while that definitely improved in the capital, their attack paid the price for it.
Hearts head coach Steven Naismith: "All our creative players had an impact today, everyone contributed, everyone was probing. It was a confident performance that I'm happy with.
"When teams are comfortable here getting a point as a good result, it means we have to be more aggressive."
Livingston manager David Martindale: "There was a lot to like in the game, albeit we probably gave away a wee bit too much territory. We defended our 18-yard box bar that moment extremely well.
"It's hard to be overcritical of the players because I thought their shape, distances and application within the game was there."
Hearts face Rangers at Hampden in the League Cup semi-final on Sunday (15:00 GMT), while Livingston travel to take on Dundee an hour earlier.
