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But the Gorgie side had Craig Gordon to thank for their clean sheet. The Scotland international goalkeeper made two fine saves from Mislav Karoglan in the first half to set up a lucrative tie against the Greek giants, with the first leg at Murrayfield next week.
Valdas Ivanauskas, the Hearts head coach, made two changes to the team that beat Siroki last week. Julien Brellier returned to the midfield at the expense of Ibrahim Tall, the defender, who had played as a makeshift midfield player during the game in Edinburgh. Michal Pospisil, the striker, replaced Edgaras Jankauskas, who picked up a hamstring injury on Monday.
Although Hearts had the comfort of a three-goal lead to take into the game, they showed early on they would not be content to sit on their advantage. In the seventh minute, after Deividas Cesnauskis had earned a free kick 30 yards from goal when he was fouled by Ivica Landeka, the Siroki defender, Roman Bednar fired in the set-piece that Vladimir Vasilj, the goalkeeper, gathered only at the second attempt.
The nervy Siroki goalkeeper then punched an inswinging Neil McCann corner backwards into his own net, but Viktor Kassai, the referee, judged he had been fouled inside the six-yard box.
In the 15th minute, Karoglan skipped past Brellier and unleashed a powerful drive from 25 yards but Gordon produced a superb diving save to push the ball away. Siroki began to assert themselves and Gordon again had to make an impressive save from Karoglan, this time diving to his left to punch away a powerful free kick from distance by the striker.
The match — if not the tie — was finely balance but the Gorgie side were careful not to commit too many forwards in their build-up. On the half-hour mark, Christophe Berra, the Hearts defender, scythed down Karoglan at the edge of the penalty area, but Wagner’s free kick rebounded off the Tynecastle wall.
Just before the interval, however, the home side created a decent chance when Branimir Anic, the defender, skipped past Takis Fyssas on the right and cut the ball back to Ronielle, who was just 14 yards from goal. But the Siroki player missed his kick before Josip Papic compounded the mistake by firing high over the bar from just outside the penalty area.
Siroki began the second half on the ascendancy, forcing Hearts back towards Gordon, but the Edinburgh side showed no sign of conceding the opening goal. A driving run by Wagner had the Tynecastle men on the back-foot, but, when the Siroki midfield player released Anic on the right, Gordon gathered the cross into the box.
The home side were pouring forward with more purpose now and, in the 50th minute, Wagner beat Berra to set up Celson just eight yards from goal. But the Brazilian’s shot was blocked by Gordon.
Hearts were living dangerously although Bednar’s dangerous cross from wide on the right may have reaped rewards if a maroon jersey had anticipated the ball coming over to the back-post area.
On the hour mark, Robbie Neilson, the defender, was replaced by Tall while Saulius Mikoliunas came on for McCann. The substitutions, however, did little to turn the game in Hearts’ favour.
In the 77th minute, Gordon again made an impressive save, tipping an angled drive from substitute Hrvoje Erceg round the post for a corner. Hearts defended the set-piece easily and, at the other end, Bruno Aguiar fired a 25-yard free kick just past the post.
The Gorgie side then welcomed the final whistle which brought with it the promise of a tie against AEK Athens in the next round.
NK SIROKI BRIJEG: Vasilj, Anic, Silic, Wagner, Papic, Pandza, Ivica Landeka, Gomes, Kovacic, Karoglan, Celson. Substitutes: Basic, Doci, Studenovic, Carvalho, Dalibor Kozul, Kvesic, Erceg.
HEART OF MIDLOTHIAN: Gordon, Neilson, Fyssas, Pressley, McCann, Aguiar, Pospisil, Bednar, Cesnauskis, Berra, Brellier. Substitutes: Banks, Tall, Beslija, Makela, Mikoliunas, Wallace, Mole.
Referee: V Kassai (Hungary).
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