The 2008 Wimbledon girls champion despatched Lucie Safarova in straight sets 7-6 6-4 to move through to the next round where she will face Maria Sharapova.
The 18-year-old flew out of the blocks to go 5-1 up in the first set, but lost four straight games only to eventually triumph in a tie-break – and she revealed the sheer enjoyment of playing in a home Games got to her.
"I am so excited, I was getting so nervous. I was 5-1 up in the first set and I sat down at 5-2 and I realised how nervous I was because I couldn't actually breathe at that point,” said Robson, who could not progress further than round one of Wimbledon this year.
“So from then on I tried to stay calm, stay focused on my game plan and that seemed to work. I always get nervous and I think that is a good thing.
“If you aren't getting nervous then I think there is something wrong with you. The crowd were amazing, I was just trying to play well.
“You miss a few balls and then you start to think 'Oh what's going wrong?' I'm just really excited right now."
Robson, who was born in Melbourne, made the quarter-finals of the Australian Open and remained critical of her performance today.
"I don't feel l actually played that well because I felt very up-and-down. In the second set my service games were much more solid, which was good.
“It's always really nerve-wracking playing for your country, I just did my best to stay calm and I managed it.
“I think it's just you put more pressure on yourself to play well because you are not just playing for yourself. But the crowd definitely helped me a lot today."
Watson was relatively untroubled as she progressed to the next round at the expense of Silvia Soler Espinosa of Spain.
British No.1 Watson won in straight sets and she admitted that she felt comfortable throughout her Court 17 match.
"It went very well, I felt pretty comfortable today and confident, and I think it showed on court,” said Watson who went two Wimbledon rounds better than her doubles partner Robson this year.
“I played well, served well but I still think I can play better which is good.
“I knew it was going to be a tough match. I've never played Soler Espinosa before but I knew she's a great player and she has been highly ranked for a long time so I am pleased with how it went and I am looking forward to my next match tomorrow."
Elena Baltacha admitted her singles career may be over after she lost to Serbian Ana Ivanovic in the second round.
And after her 6-4 7-6 defeat, the former British No.1 admitted an ankle injury may force her to retire from singles competition.
"I need to have the surgery otherwise I can't carry on with the foot the way that it is,” she said.
“I'm going to do the rehab and see how it goes.
“If I'm ready to come back in February then I will come back. If I feel that I'm enjoying life at home and I don't really want to get on another plane then yes, I will retire.
“The way that my mind is at the moment, I would like to come back. If it changes then I won't."
Baltacha later lost in the doubles alongside partner Anne Keothavong as Julia Goerges and Anna-Lena Gronefeld of Germany ran out 6-3 6-1 winners.