The 20-year-old earned high praise for defeating Czech world number 52 Iveta Benesova 6-2 6-1 on Centre Court on Monday and followed up with a solid victory in 77 minutes on court two.
Watson, who was schooled at the Florida tennis production line that is the Nick Bollettieri Academy, won the opening five games and raced through the opening stanza in 28 minutes.
The Channel Islander continued the momentum by breaking Hampton, who stands three places higher at 100 in the world rankings, in the opening game of the second set.
But the American, conqueror of 27th seed Daniela Hantuchova in round one, levelled at 2-2 before three consecutive breaks followed.
The Guernsey youngster regained her grip by breaking in the eighth game and she served out to set up a last 32 meeting with third seed Agnieszka Radwanska, who was in superb form as she destroyed Elena Vesnina 6-2 6-1.
Watson said: "I knew I had to come at her from the start and not give anything away, and I don't think Jamie was at her best in the first set. The second was tougher but I had to stay calm and focused. The crowd give you so much support and I did it for them."
Watson is the first British woman to reach the third round at SW19 since 2002 and Elena Baltacha and Anne Keothavong will look to join her on Thursday.
Jamie Baker’s Wimbledon dream was ended by Andy Roddick, although the match was not as one-sided as the 7-6 6-4 7-5 scoreline would suggest.
British number three Baker, ranked 186th in the world, worked exceptionally hard and was competitive on almost every point against the big-serving American in a rain-delayed match that had started on Tuesday and took over three hours to complete.
The Scot’s aggressive running and shot-making gave Roddick plenty of trouble, with the former world number one admitting he had been given a run for his money afterwards.
But Baker was unable to take any of the five break points he earned, with Roddick eventually sealing victory with a trademark ace after a late break in the third.
Roddick next faces Bjorn Phau for a place in the third round.
In action for Britain on Thursday are Elena Baltacha against Petra Kvitova, Anne Keothavong against Sara Errani and Andy Murray against Ivo Karlovic.