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 late on.
With extra time looming, Liverpool rallied and Suarez made amends for missing two earlier gilt-edged chances with a fine finish in the 88th minute.
It was a victory the Reds thoroughly deserved, played out against the backdrop of Friday's impending transfer deadline.
With £35million club record signing Andy Carroll conspicuous by his absence - as it transpired, finalising a loan move to West Ham - Rodgers handed a first start to 18-year-old striker Adam Morgan.
With 17-year-old Raheem Sterling having featured in the two previous games, 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.
With Rodgers having expressed a liking for "multi-functional" players, England winger Stewart Downing was fielded at left-back while Jordan Henderson, whose future has been the subject of speculation, was given a chance.
Hearts fielded the same side that started the first leg last week with captain Marius Zaliukas overcoming a thigh injury.
The Scottish side played some neat football and were not intimidated by Liverpool's reputation.
But aside from a dipping early shot wide from Callum Paterson, they lacked penetration and the hosts dominated.
Suarez tricked his way into the box but his shot was blocked for a corner.
Downing crossed for Morgan, who let the ball run for Gerrard but could not control the skipper's return inside.
Morgan's enthusiasm saw him catch Templeton with a late tackle but he escaped unpunished and grew in confidence playing in front of a fired up Gerrard.
Morgan headed back another deep cross from Downing and Suarez reached it to get a header on target but Zaliukas hacked off the line with Jamie MacDonald beaten.
Hearts appealed for a penalty when Paterson went down with Carragher in close proximity, but contact was ruled minimal.
Morgan tested MacDonald with a long-range shot as Liverpool came forward again but the goalkeeper managed to clutch the ball at the second attempt as Gerrard hunted the rebound.
Gerrard then weaved his way into the Hearts area to get in a shot but MacDonald blocked his shot - and the Scots breathed another sigh of relief when Morgan side-footed home in the 34th minute, only to have the effort ruled out as the ball had gone out before Suarez crossed.
Liverpool maintained the pressure in the second half with Jonjo Shelvey finding space to shoot wide from 25 yards.
The hosts seemed certain to take the lead in the 65th minute when Suarez, who had been goaded by the Hearts fans, timed a run perfectly to race through on MacDonald's goal.
As Manchester City's Carlos Tevez had done at the same end on Sunday, Suarez looked poised to take it round the goalkeeper and score but his touch was heavy and the chance was wasted.
Suarez's finishing ability was again brought into question just moments later, when after doing the hard part to beat Zaliukas, he blasted wide.
Sterling replaced Morgan to a huge ovation and immediately looked lively as he chased a first senior goal - denied only by a vital block by Daniel Grainger after one good run.
MacDonald tipped over a header from Skrtel but the Slovakian was ruled offside anyway.
Despite Liverpool's dominance Hearts were still only a goal away from taking the tie to extra-time.
Joe Allen escaped after Dale Carrick went down under his challenge outside the area but Sterling was punished for a push on Templeton 25 yards out.
Grainger lined up a shot but his effort was deflected for a corner off the wall.
That was a warning for the Reds and Hearts made them pay for their earlier profligacy six minutes from time.
Templeton seized on a clearance and took a couple of touches before firing at Reina.
It was well struck but the keeper should still have dealt with it, only it squirmed through his grasp.
Liverpool were forced to rouse themselves for one last push and Suarez made no mistake as he burst down the left and fired low across goal from a tight angle.