The deadlock was broken 12 minutes from time when a Martin Kelly cross was turned into his own net by Webster, a cruel blow to both the defender and his team who had provided Liverpool with a stern test throughout the entire 90 minutes.
Andrew Driver had a great chance to equalise late on but could not get a powerful enough shot off as Hearts failed to find a deserved leveller, following an intriguing game in which the SPL side looked strong for lengthy spells.
Eyebrows were raised momentarily when the teamsheets were released prior to kick-off by the omission of Andy Carroll’s name, but Liverpool manager Brendan Rodgers cleared up any question over transfer inferences that may have been drawn by explaining that the striker had been rested up after feeling a hamstring tweak in training.
With big names Steven Gerrard, Luis Suarez, Martin Skrtel and Glen Johnson all left back home to recuperate fully ahead of Sunday’s visit to Anfield of Premier League champions Manchester City, the likes of Kelly, Jonjo Shelvey, Jordan Henderson, Raheem Sterling and Jack Robinson all started and the younger names acquitted themselves well against an organised and effective Hearts side.
But it was the home team who enjoyed the stronger start as they troubled Liverpool, Arvydas Novikovas calling Pepe Reina into action from 30 yards early on and David Templeton highly impressive as he gave the away defence plenty to deal with.
Sterling gave a few brief glimpses of pace down the left but for the first 20 minutes the youngster was only afforded a few snatched moments of possession, as Hearts shone. When Liverpool did manage to bring the 17-year-old into the game more he dazzled.
First he almost forced Webster into scoring an own-goal, and then had a shot parried by Jamie MacDonald in the Hearts goal. The hosts continued to get forward too which made for an entertaining first 45 minutes, as Templeton flashed a volley not far over from inside the area and a hopeful penalty appeal was also turned away when the ball struck Jamie Carragher on the arm.
But the opportunity of the half fell to Liverpool on the stroke of half-time. It was Sterling who created it when he read a poor pass across the middle from Mehdi Taouil, and the interception put him through on goal. Unselfishly the winger squared to the better positioned Fabio Borini, but the Italian thundered the ball against the post from 12 yards when he should really have scored.
Hearts flew out for the second half and there continued to be a back and forth flow of possession and half-chances, but there was a lack of clear-cut opportunities on offer.
When the scoring was opened it was Hearts who went behind but not deservedly so, as Webster knocked the ball into his own goal when unable to adjust his feet quickly enough to clear Kelly’s cross with Borini lurking in front of him.
With little time remaining both sides continued to push, Liverpool for a second goal which would have given them a more comfortable advantage and Hearts for parity.
The home side had a golden opportunity when the ball broke loose for substitute Driver inside the area, but a slight lack of composure saw the forward get off a weak shot which failed to trouble Reina.
Callum Paterson did manage to work the Spaniard in the dying moments with an excellent volley on the angle which Reina had to palm away, but Liverpool held onto the lead which they now carry into the second leg next week.