In last season’s competition, Hearts had drawn Tottenham Hotspur and were keen to avoid a repeat of the tanking they received from the White Hart Lane side.
In the opening exchanges both keepers were tested, Jamie MacDonald denying former Rangers midfielder Charlie Adam, while Pepe Reina was forced to race from his goal to deny John Sutton a chance on goal. He had to be at his best to deny Arvydas Novikovas’ effort from 25 yards out with the Spaniard at full stretch to save it.
John Sutton and David Templeton both had chances for Hearts as they pressed Liverpool and showed their multi-millionaire opponents that they were no push overs.
One plus point for Liverpool was the play of Raheem Sterling, who was a thorn in the Hearts side throughout and nearly forced Darren Barr into conceding an own goal as he slid in to deny the winger a shot on goal.
Sterling continued to make his presence felt as struck a superb effort towards the Hearts goal but MacDonald was equal to it and saved the shot.
On 33 minutes, Liverpool should have been one goal to the good. A counter attack led by Jordan Henderson down the right flank, saw the winger fire in a cross or Borini and with the goal at his mercy, the Italian slipped the ball wide.
Despite the increased pressure from the English side, Hearts continued to have forays up front. David Templeton fired a shot just over the bar, before the home side claimed for a penalty after Jamie Carragher allegedly handled the ball in the box, however the pleas were waved away by referee Florian Meyer.
That man Borini missed another glorious chance to give Liverpool the lead after Sterling set him up with only the keeper to beat, but while the Italian beat MacDonald in the Hearts goal, his shot stuck the post and away from danger.
Into the second half and it was Hearts who continued to threaten early on, with Callum Paterson firing a powerful strike that had Hearts fans off their seats close to celebrating, but his shot failed to hit the back of the net.
With Hearts stubbornly defending, Charlie Adam tried a long-range shot which failed to test MacDonald, before Novikovas tried to show Adam how it should be done, but his shot failed to trouble Reina also.
There was heart-break for the home side with 12 minutes remaining. Kelly drove down the right flank before crossing the ball into Borini, but while the Italian missed once again, Andy Webster could not avoid the ball and knocked it into the back of the net to give Liverpool the lead against the run of play.
Into the closing stages of the match and Sterling was still proving to be troublesome but he failed to test MacDonald in the late chances that he was offered.
Hearts were given one last chance to find that deserved equaliser as Paterson fired a shot towards goal from an acute angle, but Reina was equal to it and turned it away from goal.
Brendan Rodgers’ side take the 1-0 lead back to Anfield, comfortable in the notion that many would still see them as favourites for the second leg, but they will have to put out their big guns to kill off the threat of a resolute Hearts side who never shirked under the pressure from their rich opponent.
The result was harsh on Hearts, but against the multi-million pound playboys of Anfield many expected Hearts to be on a hiding to nothing. They pleasantly surprised many tonight.