A late goal from Luis Suarez proved enough to send Liverpool into the group stages of the Europa League.
The 88th minute winner was a get out of jail card for Suarez and Pepe Reina, who had earlier allowed a shot from David Templeton to squeeze under his body.
Brendan Rodgers' side dominated in all areas but a whole host of missed chances, in particular from Suarez, prevented the Reds from adding to their one goal win at Tynecastle.
Liverpool were forced to rally late as thirty minutes of extra-time loomed. Suarez made up for two earlier misses by scoring a fine leveller two minutes from time.
The Reds were deserved victors but the win was achieved with the exception of the club's most expensive player. At half-time it was confirmed that Andy Carroll had put pen to paper on a season long loan deal to West Ham.
18-year-old Adam Morgan started, whilst 17-year-old Raheem Sterling terrorised Hearts with his cutting runs from the left flank.
After being rested for the first leg in Edinburgh, Steven Gerrard and Luis Suarez returned to the starting line up alongside Martin Skrtel, Reina and Jamie Carragher. Jordan Henderson was also recalled and Stewart Downing deployed at left back.
Hearts were unchanged from the first leg, as skipper Marius Zaliukas had recovered from a thigh injury to play.
John McGlynn's men were not intimidated by the reputation of their illustrious opponents and had a short spell of sustained play in the Reds half early. But, despite a lack of a cutting edge, Liverpool were dominant for most of the match and deservedly enter the draw for the next round.