Published Thursday, 23 August 2012
Liverpool's Reheem Sterling is challenged by Hearts' Ryan McGowan. (© PA)
An own goal from Andy Webster in the 78th minute proved the decider at Tynecastle Stadium after a difficult night for the Reds in Edinburgh.
The ball came off the defender's shin after a cross was delivered into the box by Martin Kelly.
It came as some relief for Liverpool after they squandered chances earlier in the match, the best of them falling to Fabio Borini just before half time.
He was played in on goal by Raheem Sterling, but his shot smacked against the post.
Hearts continued to press in the dying minutes and had their chance to draw level when Jamie Carragher failed to clear from a dangerous cross by Ryan McGowan.
Substitute Andrew Driver fired after turning but there was no power behind his strike, and goalkeeper Pepe Reina made the save.
Reina was again called into action late on when he dived to keep out a driving shot from Callum Paterson - but there was to be no late equaliser for the Scottish side, who will travel to Anfield for the return leg of the play-off next week.
Meanwhile the result will take some of the pressure of Carnlough man Rodgers, after he saw his team lose 3-0 to West Brom in their opening Premier League fixture at the weekend.
"First and foremost it was a win which is very important in European games, and certainly coming to a place like this with the crowd right up for it," he said.
"I thought the players were excellent.
"We spoke about our positioning at half-time and in the second half our management of the game was much better. We kept possession better and the goal came from a very good move.
"It was a good win, a difficult match for us, and it was a really good game."