Brendan Rodgers’ side dominated the second leg of their qualifying round play-off at Anfield but were punished for not adding to their 1-0 aggregate lead when Reina let a David Templeton shot squeeze through with five minutes left.
With extra-time looming, Liverpool rallied and Suarez made amends for missing two earlier gilt-edged chances with a fine run and angled finish in the 88th minute to give the Anfield side a deserved victory.
With 17-year-old Raheem Sterling having featured in the two previous games, manager Brendan Rodgers has not been afraid to give youth a chance but there was still an experienced look to his side.
Captain Steven Gerrard and star forward Suarez, both rested for the first leg at Tynecastle, were included along with the likes of Reina, Jamie Carragher and Martin Skrtel.
Liverpool’s Stewart Downing admits his team found life tough against the visitors from Edinburgh.
Midfielder Downing, who was employed at left-back by Rodgers last night, was relieved to get through to the next round.
“We knew it was going to be tough,” he told ESPN. “We made more hard work of it than we should have done.
“We were a little bit wasteful in front of goal.
“However, the manager stressed to the team ‘don’t go down under pressure’, and I think we bounced back well.
“We created lots of chances we didn’t finish though, and we have to be more clinical in front of goal. That was a lesson for us.”
LIVERPOOL: Reina, Kelly, Carragher, Skrtel, Downing, Henderson (Bornin 76), Allen, Shelvey, Gerrard, Morgan (Sterling 62), Suarez.
HEARTS: MacDonald, Ryan McGowan, Webster, Zaliukas, Grainger, Novikovas (Carrick 75), Barr, Taouil, Paterson, Templeton, Sutton (Driver 66).
Referee: Vladislav Bezborodov (Russia).