The Glaswegian giants took to the pitch for the first time since drawing 1-1 with St Mirren under the tutelage of Giovanni van Bronckhorst in the Scottish Premiership on November 12.
Van Bronckhorst was relieved of his duties nine days later before Beale was named as his successor after agreeing to leave his managerial role at Queens Park Rangers.
Beale, who received a warm welcome from the Ibrox faithful, named a strong starting lineup for his opening game against Leverkusen, although there was no sign of Connor Goldson, John Souttar, Ben Davies and Tom Lawrence who are all still recovering from injury, while Borna Barisic is still away on World Cup duty with Croatia.
Captain James Tavernier led his team out at Ibrox, and the attack-minded right-back curled a delightful cross into the box to set up Malik Tillman for a 15th-minute opener, with the Bayern Munich loanee calmly slotting a first-time finish beyond Leverkusen goalkeeper Lukas Hradecky.
Tavernier and Tillman combined again to help Rangers double their lead just five minutes later, with the former whipping a corner towards the near post for the latter to head home his second.
Leverkusen lacked a cutting edge in the first half and struggled to test Rangers' backline, while the Gers were in control of proceedings and headed into the break with a deserved lead.
Beale rang the changes at half time, with Tillman, Allan McGregor, Ryan Jack, Glen Kamara, Ryan Kent, Rabbi Matondo and Antonio Colak all replaced by Scott Arfield, Jon McLaughlin, Scott Wright, Steven Davis, John Lundstram, Fashion Sakala and Alfredo Morelos.
Rangers came close to adding a third 10 minutes into the second half when Arfield received the ball from Morelos inside the are before Hradecky denied the Canadian from close range.
Shortly after coming off the bench, Gers youngster Alex Lowry fired a curling effort narrowly wide of the post before Tavernier made a brilliant last-ditch tackle to prevent Leverkusen's Leon Pesch from scoring inside the six-yard box.
With 10 minutes remaining, Rangers were awarded a penalty after Morelos went down following a late challenge, but Tavernier saw his effort from 12 yards smack the post and roll away from danger.
However, the Gers were able to wrap up the victory with a third goal just four minutes later when Arfield slotted home a composed finish following a well-worked team move.
While Xavi Alonso's Leverkusen side offered little going forward, Beale will be delighted with his team's performance in his first game in charge, with a mixture of senior stars and young prospects gaining valuable minutes ahead of the Premiership restart.
Indeed, Rangers will get their top-flight campaign back underway when they welcome Hibernian to Ibrox next Thursday, with the Gers aiming to close the nine-point gap that currently separates them from league leaders Celtic.