Alex McLeish’s side raced into a two-goal lead after only 16 minutes through headed goals from Lorenzo Amoruso and then Shota Arveladze and never looked in danger of relinquishing that advantage, despite Eugene Dadi’s last-gasp header that restored some respectability to the scoreline for the home side.
It was the performance of Mr Rowbotham that attracted most attention, however, as he made a serious of questionable decisions that threatened to detract from Rangers’ impressive showing.
The referee chose to ignore Mikel Arteta’s stamp at Phillippe Brinquin before denying the Rangers player a clear-cut penalty when he was tripped by Marvin Andrews in the box.
Livingston were then awarded a controversial spot-kick when Roland Zarate seemed to fall unchallenged in the box but Stefan Klos made amends by saving the penalty with his legs.
Despite Dadi’s late header, Rangers held on to record a vital win ahead of next week’s Old Firm match at Celtic Park.
The Light Blues had taken more than an hour to break the deadlock the last time they travelled through to Almondvale but the large visiting support had only eight minutes to wait for a goal this time around.
Arteta swung over a hanging corner from the right and the towering Amoruso was able to leap unmarked to power a header past the exposed Alan Main for his fourth goal of the season.
With the sun at the backs, Rangers looked in the mood to pour forward from defence whenever possible, with Michael Mols leading the line once more in place of the absent Ronald de Boer.
Arveladze bagged a hat-trick the last time the sides clashed at Ibrox and he must have thought he had added to that tally when he flicked Mols’ pass under Main on the quarter-hour mark.
Not for the first time this season, however, the Georgian striker had wandered offside and the goal was disallowed.
A minute later he made amends. Arteta fed the ball wide to the in-form Neil McCann and his cross bounced dangerously between goalkeeper and defenders allowing Arveladze to stoop to nod the ball across the line from a few yards out.
With a two-goal cushion to their name, Rangers seemed to ease off for the remainder of the half and allowed their hosts to carry the game towards Stefan Klos’ goal.
It seemed a risky move considering Livingston had clawed a four-goal deficit back to 4-3 in that previous encounter between the teams last December but the Light Blues defence looked confident as they dealt with the home side’s attacking threat.
Quino had a powerful drive well held by Klos before Stuart Lovell’s shot was deflected for a corner.
Jerome Bonnissel made his first start for Rangers in the left-back role with Arthur Numan out injured and he looked keen to support McCann down the left flank whenever the occasion arose.
His over-enthusiasm almost landed him in trouble after 23 minutes when he leapt in to a tackle that took out both Barry Wilson and the corner flag but Mr Rowbotham chose only to lecture the Frenchman rather than flash a yellow card in his direction.
It was the latest in a line of bizarre decisions from the referee, who chose to book McCann for a late tackle on Julian Maidana but then waved play on when Arteta seemed to kick Brinquin as the pair lay on the ground.
The decision sent Livingston boss Jim Leishman into a fit of apoplectic rage, with his mane of unkempt silver hair standing on end even more than usual.
Livingston brought on Dadi at half-time to try to bolster their attack but it was Rangers who started the half in the ascendancy.
Within a minute, Arveladze had a double chance to add to his earlier striker, but Main blocked his first effort with Burton O’Brien hacking his follow-up attempt off the goal-line.
Play swung from end-to-end and after both Mols and McCann had been unable to convert Kevin Muscat’s precise cross, Dadi held off Craig Moore at the other end but flashed a shot wide of the target.
With Rangers looking for a third goal that would have surely killed off Livi’s challenge, Arteta burst into the box and seemed to have his legs taken from him by Andrews as he cut back inside.
Despite having a clear look at the situation, Mr Rowbotham looked unimpressed and waved play on much to the Rangers’ bench consternation.
The Light Blues thought they had grabbed a third goal when substitutes Claudio Caniggia and Steven Thompson combined for the Argentinean to tap the ball in from close range.
Offside was again the decision and as Rangers protested, the referee compounded their misery by awarding a penalty to Livingston less than a minute later.
It seemed an incredible decision -Zarate seemed to be on the deck before Craig Moore had even approached him – but Klos again proved his worth by blocking Zarate’s spot-kick with his legs.
Fernando Ricksen then almost scored a Pele-esque goal from inside his own half after Main had came well out his goal to deny Thompson.
The former St Johnstone goalkeeper was again the hero as he denied Thompson and then Barry Ferguson before Dadi grabbed a consolation goal in the last minute as he scored with a header from close range.
It was too little to late for the Almondvale side as Rangers clung on to their six-point lead at the top of the table.
LIVINGSTON (4-4-2): 1 Main; 2 Brinquin, 5 Andrews, 3 Maidana, 20 Bahoken; 14 Makel (Cherif 77) 27 O’Brien, 17 Lovell, 12 Quino (Dadi 46); 9 Zarate, 7 Wilson (Xausa 61)
Subs not used: McEwan, Camacho
Booked: None
RANGERS (4-3-3): 1 Klos; 17 Muscat, 3 Moore, 4 Amoruso, 16 Bonnissel; 2 Ricksen, 6 Ferguson, 23 Arteta; 24 Arveladze (Thompson 70), 10 Mols (Caniggia 61), 11 McCann
Subs not used: McGregor, Hughes, Malcolm
Booked: McCann (29), Ferguson (80), Muscat (83)
Referee: John Rowbotham
Attendance: 10,004
Man of the Match: Neil McCann