Rangers narrowed the gap to Celtic to six points with a single goal win over Ross County.
John Lundstram's low drive found the net 10 minutes from the start of the second half, but there were some nerves.
George had a chance to get the ball from Jon McLaughlin.
Rangers got another three points under their new manager.
For the third match in a row, the visitors head back to Glasgow having put the onus on Celtic to get back in the game.
Scott Arfield got a start after his double against Aberdeen as Rangers were forced to do without Allan McGregor, who was unwell.
Fashion Sakala was given the central striking role as Alfredo Morelos was dropped to the bench and the Zambian was wastefully wide.
The defensive frailties of Rangers' first two wins under Beale came back to haunt them as defender Harmon rose at the back post to block McLaughlin's shot from point blank range.
OwuraEdwards flashed a low drive across the face of goal.
Lundstram, who started in the middle of the park after recovering from a knock, fired low past the goalkeeper from 18 yards to give Rangers the lead.
After Sakala slid in from 10 yards, Laidlaw's legs came to the aid of him.
The precarious nature of the lead had Rangers fans in a state of shock as Rabbi Matondo was denied one-on-one by Laidlaw.
The fact that Rangers had to come from behind to win their two games against Aberdeen and Hibs shows how much work needs to be done if they are to challenge for the title.
Without the injured Antonio Colak, Rangers lack a forward focus and are still searching for someone capable of opening up a tightly packed defence for whoever leads the line.
They will take heart from keeping the visiting fans on the edge of their seats until the final whistle even though they haven't beaten Glasgow in 21 meetings.
Considering Rangers had found the net 28 times in their previous seven meetings, limiting them to a single goal could be seen as a moral victory.
Keeping the pressure on Celtic will be one of the positives.
Rangers and Motherwell are both playing on Wednesday.