After beating the Scottish side 1-0 in the first leg, the Reds survived a late scare at Anfield to secure their progression to the group stages of the Europa League
Brendan Rodgers' side were in control but lacked cutting edge and it looked as if they would be made to pay as Reina allowed David Templeton's strike to squirm past him. However Suarez saved the day with a late equaliser from a tight angle.
Suarez partnered Adam Morgan up front on the 18-year-old's first competitive start for the Reds, while Raheem Sterling dropped to the bench despite impressing in the first leg and against Manchester City.
Hearts keeper Jamie MacDonald returned after missing the first leg for family reasons, while the man who replaced him at Tynecastle, Peter Enckelman, was suffering from a shoulder injury leaving teenager Jack Hamilton on the bench.
The first real opportunity of the game went the hosts' way just before the 15 minute mark. Stewart Downing, who started the game at full-back, found Morgan with a deep cross, the youngster nodded the delivery back across goal towards Suarez but the forward's close-range header was saved and then hacked away.
The Reds continued to see the better share of the ball, but found breaking down the Hearts' back-line no easy task, Martin Kelly overhit his cross when the hosts did manage to break free on the right flank.
With the half-hour mark approaching, the visiting supporters had a penalty appeal correctly turned down as Callum Paterson fell under pressure, but no contact, from Jamie Carragher.
The better chances continued to fall to the home side as Morgan's low drive was initially spilled by MacDonald, but he regathered before Steven Gerrard could pounce.
The Liverpool captain then embarked on a brilliant solo run that saw him break clear before attempting to dink the ball past the onrushing keeper with his left foot, but the effort was matched by an equally impressive save.
With 15 minutes until the break, Morgan had the ball in the net after tapping home into an empty net, however the referee deemed that the whole ball had already crossed the line before Suarez's sliding cut-back, denying the teen a dream goal on his European bow.
The game took a while to get going again in the second-half, as the Reds continued to control the match without creating much in the final third.
After the hour mark, the home side should have taken the lead. Suarez beat the offside trap to latch onto Jordan Henderson's through ball, the striker then rounded the keeper but hesitated and eventually saw his shot deflect onto the post. Moments later the forward wasted another good position after lashing wide with his left foot from inside the box.
Sterling's introduction soon after helped inject some pace into Liverpool's play, the tricky winger halted at the last by a super tackle from Danny Grainger following a winding run before Gerrard's follow-up was saved by MacDonald.
With less than 10 minutes to go, Reina, who had very little to do for the majority of the game, made a huge error that gave Hearts hope of extra-time. Templeton fired a tame shot from outside the area straight at the Spaniard, however, the keeper failed to hold onto it as the ball found its way across the line and levelled the aggregate scores.
Liverpool responded perfectly though, as they broke down the other end with Suarez, who completed an individual run with a powerful finish past MacDonald from an acute angle, sending the Reds into the group stages of the Europa League.