Hearts skipper Alim Ozturk rattled the crossbar as the visitors went agonisingly close to securing a Europa League second qualifying round success in the searing heat of Malta.
However, the Jambos will be confident of finishing the job at Tynecastle next week after dominating in their 0-0 stalemate against a limited Birkirkara side.
Conor Sammon also saw a goal contentiously disallowed after just thee minutes, while Jamie Walker was a constant threat.
Hearts' only regret as they touch down in Edinburgh on Friday morning will be that they failed to bring a lead back with them.
Despite the signing of Viktor Noring and the temptation to utilise the experience and calm head of fit-again Don Cowie, head coach Robbie Neilson named the same side which saw off FC Infonet in Tallinn last week.
Birkirkara, meanwhile, pinned their attacking hopes on Vito Plut, the gifted striker who helped dump Hibernian out of Europe in 2010 while on the books of Maribor.
Mercifully for the visitors, the pitch was in shade by the time the match began at 8.30pm local time, however the temperature was still 27 degrees celsius with suffocating humidity.
Hearts wasted no time in adapting to the conditions and thought they had produced a dream start. Prince Buaben bundled the ball into the box and, after a fortunate ricochet, Sammon reacted to slot home from close range.
The assistant referee's flag cut the celebrations short, with the big Irishman deemed to have been offside.
Walker, who racked up an astonishing four assists against FC Infonet last week, was proving a menace again and curled a drive just wide from the edge of the box.
There was a major blow for the Gorgie men when the injured Perry Kitchen had to be replaced by Cowie on the half-hour mark.
Nevertheless, Hearts were back on the front foot prior to half-time when Buaben delivered a tantalising cross to the back post where Walker was waiting, however the Scotland Under-21 cap saw his miscued effort trickle into the arms of Miroslav Kopric.
A Ryan Scicluna shot, which rippled the side-netting, was as close as the hosts came in the first period.
Igor Rossi met a Walker corner kick to force a sharp, if overblown, save from Kopric as the second half started in the same manner as the first.
And Hearts were the width of the woodwork away from taking a lead back to Edinburgh when Ozturk unleashed a stunning shot from 35 yards which had Kopric beaten.