Four of the summer signings were on target with their first competitive goals for the club as Sam Lammers, Danilo, Abdallah Sima and Kieran Dowell all found the back of the net as Gers picked up three points at home.
From the midweek UEFA Champions League qualifier against Servette, Beale named two changes to his side with Jose Cifuentes and Leon Balogun coming into the starting XI in place of Ryan Jack and Connor Goldson who were rested for this match.
It was a starting debut for Cifuentes, who joined the club earlier this month, while Balogun also made his first competitive start since making his Rangers return.
Beale started with Butland in goal and a back four of James Tavernier, Leon Balogun, John Souttar and Borna Barisic.
Cifuentes came into midfield alongside Nico Raskin and Todd Cantwell, while the manager stuck with the attacking line-up as midweek with Sam Lammers, Cyriel Dessers and Danilo completing the XI.
It was Rangers who had the first sight of goal in this match as they looked to make a strong start in front of a packed Ibrox. Tavernier’s cross from the right was flicked into the path of Danilo by Cyriel Dessers but the Brazilian’s strike curled just over the target.
Dessers came close inside the opening 10 minutes as he was alert to beat Shamal George to the ball and raced into the box but defender Luiyi De-Lucas was on hand to block the strike.
The early pressure paid off, however, and Rangers were ahead as a neat forward move saw Beale’s men weave through Livingston’s back line with just 10 minutes on the clock. Cantwell was able to beat the defender inside the box with his shot blocked by George but Sam Lammers followed up to send a powerful right-footed strike into the back of the net for his first Scottish Premiership goal.
A set-piece provided Rangers another opportunity shortly after as the Livingston defence were unable to deal with James Tavernier’s free-kick into the box with the ball breaking for defender John Souttar but he was unable to keep his strike down as it drifted over the bar.
The Light Blues were looking dangerous in attack, with Cifuentes next to test Shamal George as his blistering shot was pushed wide by the Livingston number one.
From the resulting corner, Cifuentes found the target with a good finish as he got on the end of a Borna Barisic set-piece but the goal was disallowed for handball following a VAR check.
A Livingston free-kick saw Stephen Kelly whip the ball into the box, with Cyriel Dessers able to head the initial ball away from goal before Holt’s follow-up shot was off target for David Martindale’s men.
Before the break, Rangers had a good opportunity to add a second as Cifuentes fed the ball out wide to James Tavernier, who delivered a cross into the area, but Cyriel Dessers’ header was held by Shamal George.
Into the second-half, Danilo saw a good strike pushed away by George with Dessers doing well to pick up the rebound to send the ball back across the face of goal but Lammers’ flick was just wide.
From a corner, Butland was called into action as Andrew Shinnie hit a strike at goal from the edge of the box, but the Rangers goalkeeper managed to push the effort away. Just seconds later Shinne picked up on a loose ball in a dangerous position, but Butland did well again to get a touch on the ball to turn it behind for a corner.
Dessers saw a shot blocked for Rangers as Beale’s men looked to increase their advantage in this match, before Jose Cifuentes found Danilo in the box but his close-range shot was over the bar.
With just over 20 minutes of the game remaining, Beale turned to his bench for the first time in this match with Rabbi Matondo and Abdallah Sima introduced in place of goalscorer Sam Lammers and Cyriel Dessers.
The two subs linked-up shortly after with Matondo doing well to feed the ball into the path of Sima but Shamal George matched the strike and blocked the shot.
With 78 minutes on the clock, Danilo doubled Rangers’ advantage with his first goal for the club. Borna Barisic picked the Brazilian out in the box with a lovely cross which he managed to get his head to and send beyond George.
It was three for Rangers just minutes later from a set-piece, Danilo’s shot came back off the post from a corner with Abdallah Sima alert to the rebound and cooly finished low beyond George for his first competitive goal for the club.
It was a strong end to this match for Rangers and Kieran Dowell, who was introduced minutes earlier, netted his first for the club as the match approached the final minutes. Rabbi Matondo broke up the pitch at pace to feed in the midfielder and it was a fantastic finish from Dowell as he drilled a powerful strike beyond George to give the Light Blues a four-goal advantage.
RANGERS: Butland, Tavernier, Balogun, Souttar, Barisic, Raskin (Lundstram, 81), Cifuentes (Sterling, 81), Cantwell (Dowell, 81), Lammers (Matondo, 70), Dessers (Sima, 70), Danilo.
Subs: McCrorie, Hagi, Roofe, King.
Livingston: George, Devlin, Obileye, De-Lucas, Brandon (Nottingham, 70), Shinnie, Holt, Montano (Ledingham, 70), Sangare (Guthrie, 46), Nouble (Bradley, 86), Kelly (Mackay, 76).
Subs: Hamilton, Penrice, Parkes, Boyes.
Referee: Don Robertson.