The American, who played in the semi-finals of this competition for PSV Eindhoven two years ago, lashed a 20-yard shot past FK Zeta goalkeeper Sasa Ivanovic in the 81st minute to extend Rangers' aggregate lead to 3-0 after last week's victory at Ibrox.
Beasley and team-mate Jean-Claude Darcheville had earlier experienced some racist taunting from the home crowd on a night which was otherwise apparently trouble-free for Rangers.
• Smith thrilled by new boys
Kris Boyd started on the bench for Rangers in Montenegro as they looked to protect a 2-0 first-leg lead in their Champions League second round qualifier against FK Zeta.
The striker was struggling with an ankle injury ahead of the game, with Darcheville fielded as the only out-and-out striker, with Lee McCulloch and Beasley for support.
Rangers were without right-back Alan Hutton, sent off in the first leg, and Kirk Broadfoot filled in. Charlie Adam, who failed to shine in the first leg, was replaced - as he was at Inverness on Saturday - by Kevin Thomson.
The attention of UEFA was on the Rangers supporters, a minority of whom have let the club down with sectarian chanting in recent European games, and in Saturday's Clydesdale Premier League match at Inverness.
Zeta made just one change, with Nenad Djurovic coming into the defence at the expense of Milan Vuckovic.
They approached the match at the Gradski Stadium - not their regular home, but chosen to accommodate the largest crowd - with the conviction that Rangers' lead could be overturned.
After a quiet start, the first threat came from Slaven Stjepanovic down the left, but Broadfoot dealt well with the danger.
McCulloch shot well wide from 25 yards in the ninth minute, before Beasley shot just wide from 20 yards.
The first booking went to Blazo Igumanovic in the 23rd minute for a late tackle, before Stjepanovic shot over.
Cetkovic wriggled past three defenders and set up Bojan Ivanovic for a low shot which McGregor had to get down quickly to gather.
McGregor then carelessly missed a cross before gathering after a high bounce.
Broadfoot failed to make the most of a headed chance, while Beasley remained dangerous coming in from the right flank, winning a couple of free-kicks.
Miroslav Kaludjerovic made a last-ditch challenge to deny Darcheville as the Frenchman threatened just before the break.
Djurovic was booked in the fourth minute of the second half for a reckless challenge on McCulloch, sliding in near the halfway line after the ball had gone.
The hosts made their first change in the 56th minute when the injured Djurovic was replaced by Ivan Knezevic.
Rangers collected their first booking two minutes later with Broadfoot the offender, and Darcheville was soon replaced by Nacho Novo.
McCulloch moved into the central attacking role, with Novo and Beasley his supporting cast.
Zarko Korac wasted a decent chance to halve Rangers' lead when he headed over the bar from eight yards.
McGregor then helped out his defenders with a punched clearance after Ivanovic threatened to get on the end of a long pass over the top.
Ivanovic went down and the crowd briefly demanded a penalty, but Italian referee Paolo Dondarini saw nothing wrong.
Dondarini turned down appeals from Broadfoot soon afterwards when the defender, on a burst forward, stumbled over a challenge.
McCulloch's shot after a laboured build-up was still rising when it cleared the bar - and the same player headed over the bar from Rangers' next chance.
Zeta might have had a penalty in the 75th minute when Stjepanovic went down under the challenge of Broadfoot.
He looked to have been caught but made his protests too vigorously for the referee, who booked the striker.
Beasley netted the only goal of the night in the 81st minute, darting in off the left flank and drilling a low right-footed shot just inside the left post.
Zeta's flapping goalkeeper Sasa Ivanovic dropped a Barry Ferguson cross as Rangers pushed for another goal, before Novo sliced a shot well wide after Thomson picked out his run.
Substitute Adam, on for Thomson, slashed another shot off target, but Rangers cruised to the final whistle.
They await either Red Star Belgrade or Levadia Tallinn in the next round, with the second leg of that tie in Estonia on Wednesday evening.
Smith thrilled by new boys
Rangers manager Walter Smith's summer spending spree looks like paying for itself after DaMarcus Beasley and a host of new boys shone in the Champions League victory over FK Zeta.
American winger Beasley is proving a snip for the £700,000 Rangers paid to PSV
Eindhoven and capped a fine performance in Podgorica with a terrific winning
goal to secure a 3-0 aggregate victory.
But there was also an outstanding performance in defence from Spanish
centre-back Carlos Cuellar, while former St Mirren captain Kirk Broadfoot gave a
battling display at right-back.
Lee McCulloch, who joined from Wigan, and former Bordeaux striker Jean-Claude
Darcheville also occupied the Zeta defence as Rangers eased into the final round
of qualifying.
'It wasn't easy for us in this game,' said Smith, who has spent more than
£7million on new additions this summer and is not finished yet in the transfer
market.
'Zeta did their best on their European debut, but we proved that we are the
better side in this tie, and that we deserved to be in the next round.
'We have a good team, the boys did well and it was important for us both to
reach the next round, and to continue with our victories at the start of the
season.
'Our squad has plenty of new players, and I must say they did well.
'It's important for us to play well, not to make mistakes, and we've proved
at the start of the season that we are on the right track.
'Now, we must focus on our next task.'
Red Star Belgrade and Levadia Tallinn contest the second leg of their second
qualifying round match tomorrow night in Estonia, with Rangers lying in wait for
the winners.
If Smith's side can get through their next test, then the thrill of competing
with Europe's elite - and a massive pay-day - await.
Smith said: 'When they finish their second leg, we'll see what will happen
next.'
Zeta coach Slobodan Halilovic criticised his team for abandoning their match
plan.
Halilovic said: 'I'm proud of my players, but I must say they missed their
chance because of trying to beat Rangers by playing a style they're not used to,
and which they weren't told to do.
'We're a technique-based type of squad, we won the title with fast play, fast
moves, quick attacks, and today we've tried something else, even though it
wasn't our agreement in the locker room.
'I must congratulate Rangers for the win, and, if Red Star Belgrade reach the
next round of qualification, I think it is the Glasgow side who will be
favourites in that clash.'
Zeta 0 - 1 Rangers
