Ninth seed Konta, 25, produced a confident display to beat 19-year-old Naomi Osaka of Japan 6-3 6-2.

Watson had five match points but was knocked out 2-6 7-6 (7-3) 10-8 by American qualifier Jennifer Brady.

Edmund, hoping to join Andy Murray and Dan Evans in the last 32, lost 6-2 6-4 6-2 to Spain's Pablo Carreno Busta.

Clinical win for in-form Konta

Konta, who will now face Denmark's 17th seed Caroline Wozniacki on Saturday, faced one of the most promising players in the women's game.

The big-serving Osaka, ranked 48th, had a chance to break Konta in the eighth game but missed a forehand and then looked on helplessly as the Briton fired down two aces to hold serve.

Konta took advantage of her opponent's loss of focus to break to love and then served out the opening set in clinical fashion.

The Briton dominated the second set to secure her 10th win of 2017.

"I love playing on these amazing courts and I'm looking forward to staying here as long as possible," she said.

Analysis - Konta a serious contender

Former Fed Cup coach Judy Murray on Radio 5 live sports extra

Johanna Konta is looking every bit the contender. She has one of the best serves in the women's game, moves well, defends much better and plays well off both sides.

She looks confident, determined and focused. She has a strong team in her corner and is in a very good position to go far in this competition.

Watson fails to take her chances

Watson, 24, should have joined Konta in the third round but was unable to clinch victory against the world number 116.

The British number two, ranked 35 places higher than Brady, took the first set without any fuss and was on course to win in straight sets, only to be broken when serving at 5-4.

She lost the tie-break and from there her 21-year-old opponent grew in confidence during a final set which lasted 86 minutes.

Watson had two break points in the fourth game, five more in the fifth, which she led 40-0 but failed to see out, and two more in the eighth but Brady survived them all.

At 6-5, the Briton had three match points on Brady's serve but squandered all of them as the American levelled.

Watson had her fourth and fifth match points at 8-7 but two strong serves ensured Brady again held on.

Watson served a double fault to hand Brady a 9-8 lead and although the Briton saved two match points on the American's serve she could not stop a third as her opponent sealed victory.

Edmund outclassed by Carreno Busta

The British number two produced an impressive victory to reach the second round but was unable to maintain that form against the 30th seed.

Edmund, 22, made too many errors and could not match the power of his opponent's serve, as he lost in an hour and 46 minutes.

He won the first game of the match on serve but then lost the next five.

At 5-2, Edmund called the trainer for treatment on his left foot, but it did not affect the momentum of the match as he netted a forehand on set point in the next game.

Edmund failed to take his first break point in the second game of the second set, and then double-faulted to hand Carreno Busta a break in the seventh game.

Edmund had chances to level the set in the 10th game, but Carreno Busta produced two big serves and took the set after surviving two further break points.

Two unforced errors and a double fault handed the Spaniard a break in the fifth game of the third set and the contest was effectively over when Carreno Busta got a second break two games later.