The 42-year-old received a warm welcome from the Ibrox faithful ahead of his first competitive game in charge of the club, but the Gers made a slow start to the contest and were behind after eight minutes courtesy of a Ryan Porteous header from a corner.
Rangers responded in the 15th minute when Fashion Sakala drilled a low strike through the legs of goalkeeper Rocky Bushiri, but Hibs immediately regained the lead less than a minute later when Kevin Nisbet - playing his first match since February after recovering from injury - running in behind the Gers backline before smacking a shot from inside the area high into the net.
Indeed, the hosts were trailing at half time, but following a "nice chat" in the dressing room, Beale got a response from his team and they equalised in the 58th minute when Malik Tillman rose to head on a James Tavernier corner before Ryan Jack reacted first to poke the ball home on the goalline.
Just four minutes later, Rangers took the lead for the first time, with Tillman involved again to set up Alfredo Morelos to slide the ball past Bushiri from around eight yards out.
Rangers grew in confidence and they managed to see out the game to help Beale secure his first three points in the dugout, moving his new side to within six points of Premiership leaders Celtic.
Beale admitted after the game that there was a lot of "anxiety" around his Rangers side, but he believes the half-time team talk helped to turn their fortunes around.
"We had a nice chat at half time and said to take the emotion out the game and play the game for what it was," Beale told BBC Scotland. "The first time the ball went near our goal, it went in.
"Then everyone gets anxious and people take too many touches, so I asked them to go back to the style we practise every day. I said there would be chances in the second half.
"The reality that hit me tonight is there's a lot of anxiety to get through, but the character of the team is good and we dominated in the second half and we deserved to win the game."
Beale added: "We need to improve on set plays. We lost Leon King this morning to illness. That wasn't ideal. He was in the team.
"[Antonio] Colak was in the team and, at the end of the training yesterday, he had a problem with his calf. I've had to ask John Lundstram to help us do a job and I'm asking James Sands as a young player to play centre-back.
"Connor [Goldson's] been back in training for two days and Ben Davies three. I felt I could get away with it tonight based on the performance against Bayer Leverkusen (who Rangers beat 3-0 in a friendly last Saturday) and I just about did.
"The players have had a lot thrown at them in the last couple of weeks. It was not anywhere near what I wanted it to look like. We've got a lot of work to do."
Rangers now have five days to prepare for their next Premiership encounter against Aberdeen at Pittodrie next Tuesday night.
Meanwhile, Rangers confirmed before their victory over Hibs that defender Leon King and midfielder Ianis Hagi have both signed contract extensions with the club.