The Scottish Premier League side now has it all to do at Anfield in a week's time after defender Andrew Webster diverted a Martin Kelly cross into his own net late in the game.
In a month when Edinburgh hosts its world famous arts festival, Liverpool set about a fringe show of its own, with squad players such as Jack Robinson, Jonjo Shelvey, Raheem Sterling and Jay Spearing all starting.
This was a European game in name only: no seas had been crossed and the tackles were as uncompromising as anything you might see in the Football League. Just ask the photographer who was accidentally taken out by a rampaging Sterling early in the game.
In terms of goalmouth action, the hosts took the early initiative. Arvydas Novikovas made Pepe Reina think, John Sutton should have done better from eight yards and David Templeton was dynamic but wayward with a shot from inside the box.
At the other end Spearing powered an effort from distance, but it was saved and his wait for a first Liverpool goal continued.
The only sign of Steven Gerrard was on the cover of the matchday program, while Martin Skrtel, Glen Johnson and Luis Suarez were also told to watch the match at home ahead of Sunday's encounter with Manchester City.
They will have seen their teammates — operating with a diamond midfield spearheaded in large parts by Shelvey – grow into the game as the first half progressed.
Sterling made the goalkeeper work with a trademark cut inside and shot, Fabio Borini was played through by Shelvey only to be denied by stopper Jamie MacDonald. A lovely pass from Jordan Henderson then invited Borini to shoot but again the Italian misfired.
Templeton volleyed over for the home side but the best chance of the half fell to Borini after a superb interception from Sterling, who was unselfish in presenting the opportunity to his Italian teammate, but might have regretted it after watching the ball clatter against the post.
Liverpool and Hearts had never previously met in competitive action, and the home fans soundtracked this small note of history with a level of noise and fervour rarely witnessed in the Premier League these days.
It was their men who created the first opening of the second period, Callum Paterson volleying close from a tight angle. Charlie Adam then whacked the hoardings from long range.
It wasn't long before Brendan Rodgers made changes: Robinson replaced at left-back by Stewart Downing, and then Spearing making way for Joe Allen.
But it was one of the starters who finally molded an opener on 78 minutes, Kelly driving with ambition down the right after a pass from Henderson. His low cross was difficult to defend, and when Borini failed to make contact, the ball ricocheted off Webster and into the net.
Moments later Sterling weaved across the edge of the box, looking for a chance to make it 2-0 as the game reached a conclusion, but his eventual shot was weak.
Hearts almost crafted a leveler with seconds to spare when Ryan McGowan surged forward and fed Andrew Driver in the six-yard box, but the substitute's composure let him down and Pepe Reina gathered.
Paterson was denied by Reina at the death and that was that until next week.
Photo via LiverpoolFC.com
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