Making his European debut for the club, the American international cut in from the left to drill a low shot past Sasa Ivanovic with nine minutes remaining and secure a 1-0 victory on the night.
Added to the goals scored by David Weir and Lee McCulloch at Ibrox, Walter Smith’s side ran out 3-0 aggregate winners and now await the winner of tomorrow’s second leg clash between Red Star Belgrade and Levadia Tallinn.
On a humid night in Podgorica the Light Blues produced a professional performance against a resilient side, who caused numerous problems over the 90 minutes.
Although there was always the feeling Gers could step up a gear, Zeta enjoyed the better chances despite being unable to take any of them.
One real sour note from the game was monkey chanting by the home support directed at Jean-Claude Darcheville and DaMarcus Beasley and this unacceptable behaviour simply must not go unpunished.
With a double change to the side that beat Inverness, Walter Smith certainly wasn’t intending to sit back in the Pod Goricam Stadium.
But with a valuable lead already in the bag the instructions were clearly to protect that first and foremost.
After setting up two last weekend, McCulloch was once again a key player for Gers and tried a speculative shot from long range after nine minutes but it flew high and wide of the Zeta goal.
The former Wigan star was at the heart of an excellent move on 11 minutes, playing a one-two with Beasley before the American curled wide.
Zeta showed in the first leg at Ibrox they are much more competent than people had expected and Slaven Stjepanovic should have done better after 25 minutes.
Following fine build-up play around the Rangers box, the ball was laid back to the midfielder and he opted for power, smashing his shot high into the stand.
It was a good chance to pull a goal back and one the home side should have taken.
The Montenegrin champions continued to press and forced Allan McGregor into a good save after half an hour.
Marko Cetkovic, by far and away the stand out player in this side, surged forward and overcame three challenges to feed Bojan Ivanovic bursting into the area. The left midfielder kept his cool to drill a low shot, but McGregor smothered well.
It was another warning and the Rangers number one did little to settle his side’s nerves a minute later when he completely missed a cross ball, before collecting at the second attempt.
Carlos Cuellar made a fantastic interception after 53 minutes when he read Korac’s run to cut out a through ball before the hitman could pull the trigger.
Kirk Broadfoot was unlucky to pick up the first booking for Rangers, just before the hour mark after a clumsy foul on Stjepanovic, despite it being his first miss-timed tackle of the night.
The Zeta forward was at the heart of things again on 64 minutes and McGregor had to rush off his line to punch clear Khezevic’s cross.
Nacho Novo was now on in place of Darcheville and McCulloch should have done better to direct his header back across goal, but nodded wide.
Cuellar was lucky to escape punishment with 15 minutes remaining when he looked to have fouled Stjepanovic in the box, but play was waved on. The Zeta forward received a booking for his furious
protest at the decision not to award a spot kick.
The goal finally came for Rangers after 81 minutes when Bealsey, who switched side’s following Novo’s introduction, cut in from the left to drill a low shot past Sasa Ivanovic.
It was his first goal for the club and a crucial strike to put Gers three goals ahead on aggregate.
The European adventure continues and Belgrade or Tallinn now awaits Walter Smith’s side in the next round.
FK ZETA: FK ZETA: S Ivanovic; Radulovic, Kaluderovic, 7 B Ivanovic (Bolevic 61), Markovic, 10 Cetkovic, 11 Stjepanovic, 13 Durovic (Khezevic 56), Tumbasevic, Igumanovic, 33 Korac
SUBS NOT USED: Mustur, Vuckovic, Marinkovic, V Pelicic, Z Pelicic,
BOOKINGS: Igumanovic 22, Stjepanovic
RANGERS: 1 McGregor; 21 Broadfoot, 24 Cuellar, 3 Weir, 5 Papac; 7 Hendami, 6 Ferguson, 8 Thomson (Adam 86); 27 McCulloch, 20 Beasley; 19 Darcheville (Novo 60)
SUBS NOT USED: 25 Carroll, 18 Murray, 15 Gow, 23 Sebo, 9 Boyd
BOOKINGS: Broadfoot 58
REFEREE: Paolo Dondarini (ITA)
ATTENDANCE: 15, 000