The home side's performance was far from convincing at times but goals from David Weir and Lee McCulloch secured a crucial victory, despite Alan Hutton's red card midway through the second half.
Rangers should have been ahead with just seven seconds on the clock. Barry Ferguson's pass from the kick-off found McCulloch, who released Kris Boyd through the middle into the box.
The striker raced past two Zeta defenders before teeing up the shot to nestle in the bottom corner but could only look on in disbelief when his left-footed effort cracked off the outside of the post.
Pirlo eyes final repeat
A less-than-inspiring display from Charlie Adam in the opening 45 minutes cost him his place for the second half.
He was replaced by Nacho Novo at the break, the Spaniard slotting into the right of midfield and McCulloch shifting to the left.
Shortly after the restart Boyd again squandered a gilt-edged opportunity in front of goal.
The breakthrough came in fortunate circumstances for Rangers with 54 minutes gone.
A Zeta clearance fell to the feet of Weir 25 yards out, who lobbed the ball back into the box.
Darcheville and Ivanovic clashed on the line in their attempts to get to the ball, both missed, and Weir's effort trickled into the back of the net.
The home side were reduced to 10 men with half an hour left to play when Hutton picked up two yellow cards in the space of 60 seconds, the second for encroaching at a free-kick.
Despite numbers now being in Zeta's favour, Rangers found the back of the net again after 72 minutes.
Ferguson's free-kick was met by the head of McCulloch at the back post, who nodded into the net from close range as Novo successfully held off a Zeta defender.
Elsewhere, Sarajevo produced the biggest surprise of the night when they won 2-1 at Belgium's Racing Genk.
Veldin Muharemovic grabbed the winner for the Bosnians four minutes from time to leave Genk facing a tricky task in next week's second leg if they are to reach August's third qualifying round, which will include clubs such as Liverpool and Lazio.
Steaua Bucharest snatched a 1-0 win in Poland at Zaglebie Lubin. Sweden striker Marcus Allback, who scored when FC Copenhagen beat Manchester United in last season's group stage, repeated the feat in their 1-0 home win over 10-man Beitar Jerusalem.
Fellow Scandinavians Elfsborg of Sweden, who beat Northern Ireland's Linfield in the last round, also managed a 1-0 win at Hungary's Debrecen.
Oleksandr Gladkiy and Brandao netted either side of half- time to help big-spending Ukrainians Shakhtar Donetsk put one foot in the third qualifying round with a 2-0 win at Armenian champions Pyunik.
The impressive Gladkiy, one of a host of recent signings including Mexican striker Nery Castillo, beat Uruguayan debutant Ignacio Javier Bordad Lopez from close range only minutes after the substitute goalkeeper had entered the field.
Finnish champions Tampere United beat Levski Sofia 1-0 at home through Tomi Petrescu's tap in on 16 minutes after a day of heavy rain. The Bulgarian title holders, looking to reach the group stage for the second successive year, otherwise dominated.
The seven remaining first legs take place on Wednesday.
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