Darren Randolph was the Republic of Ireland's hero as they returned from Denmark with a clean sheet in a 0-0 draw after surviving a stern test of their World Cup credentials.
The Middlesbrough keeper made a double save from Jens Stryger Larsen and Andreas Cornelius and then saw Pione Sisto fire wide after he had repelled Christian Eriksen's well-struck effort at the Parken Stadium in Copenhagen.
Ireland created little of note with full-back Cyrus Christie forcing Kasper Schmeichel into his only genuine save, but return to Dublin for Tuesday night's second leg with their fate still in their own hands.
The arrival of Nicklas Bendtner as a 72nd-minute replacement for Sisto got the home fans off their seats, and he was followed seconds later by Shane Long, who replaced Daryl Murphy.
Arter went down in some discomfort after a coming together with Bendtner four minutes later, but was able to continue after treatment, much to the annoyance of the home fans, who were aggrieved at the award of a free kick.
The Bournemouth midfielder, one of 10 Irishmen to go into the game on a booking, was relieved to see referee Milorad Mazic keep his card in his pocket after he had upended William Kvist.
The visitors went close at the death when Duffy headed a Brady free kick straight at Schmeichel, but Randolph had to tip Yussuff Poulsen's header over the bar seconds later and substitute Glenn Whelan sliced just past his own post as he attempted to clear Larsen's last-gasp effort.
The two teams meet again on Nov. 14 for the decisive second leg in Dublin to determine who will advance to the 2018 World Cup.