The impressive Court One victory by Britain's number one on Tuesday has seen hopes rise that the teenager can make further inroads into the draw.
With a second-round clash against Colombian Mariana Duque-Marino to come on Thursday, Murray hopes to see Robson stay at the peak of her game.
Murray, mother of British men's number one Andy Murray, told Radio Wimbledon that Robson has the ability to lift her performance when she encounters the biggest stars in the game.
"She's played big games before and she always rises to the big occasion which is a great thing," Murray said.
"She's only 19 - I think people forget that because she's been around for a long time since she won the junior event when she was only 14.
"It's a great win for her and she's going to be dangerous to whoever comes across her in the draw if she continues that kind of form."