Watson, 22, shrugged off the loss an opening set tie-break to roar into the last eight with a 6-7(6) 6-4 6-2 victory in one hour and 56 minutes.
Former world number one Caroline Wozniacki was happy to be back on grass and enjoying her game again after easing through.
"The grass really suits me", said the Dane following her 6-3 6-3 win over unseeded American Sloane Stephens. "I like the fast ball and pace I get from my opponent's shots.
"I just enjoyed it and I played well out there," said Wozniacki, who suffered a shock first round defeat on the slow clay of the French Open last month.
"I held my composure and I served well. I'm pleased with how I played."
Eighth-seed Wozniacki now faces Italian Camila Giorgi who has played over five hours of tennis in two days after two marathons.
She beat fourth seed Victoria Azarenka of Belarus in three sets in round one, and on Wednesday came through against Britain's Johanna Konta 1-6 7-5 7-5 after saving a match point.
In round one, Russian Anastasia Pavlyuchenkova put out the top seeded Pole Agnieszka Radwanska but came unstuck against her round two opponent and another Russian Ekaterina Makarova 6-3 6-3. Makarova's last eight opponent is Kerber.
The other quarter-final is between American Lauren Davis, who beat Daniela Hantuchova of Slovakia, 6-3 6-3, and Madison Keys. American Keys enjoyed a 7-5 7-6(9) win over Elena Visnina of Russia.
In the men's event, top seeded Frenchman Richard Gasquet overcame the tough challenge of Australian Bernard Tomic 6-4 3-6 6-3 but fourth seed Guillermo Garcia-Lopez of Spain was beaten 6-2 7-5 by Denis Istomin of Uzbekistan.
Women's second round results
Annika Beck (Germany) beat 1-Simona Halep (Romania) 5-7 3-2 (Halep retired)
Elina Svitolina (Ukraine) beat 6-Kirsten Flipkens (Belgium) 7-6(4) 6-4
Yaroslava Shvedova (Kazakhstan) beat Michaella Krajicek (Netherlands) 7-6(6) 7-6(4)
Coco Vandeweghe (US) beat Vania King (US) 6-7(6) 6-0 2-1 (King retired)
Zheng Jie (China) beat 4-Carla Suarez Navarro (Spain) 7-5 0-1 (Suarez retired)
8-Klara Koukalova (Czech Republic) beat Mona Barthel (Germany) 6-2 7-6(6)
Men's second round results
3-Feliciano Lopez (Spain) beat Tobias Kamke (Germany) 7-6(10) 7-5
Jeremy Chardy (France) beat Carlos Berlocq (Argentina) 6-4 7-5
Julien Benneteau (France) beat 6-Gilles Simon (France) 6-3 6-4
Sam Querrey (US) beat Victor Estrella (Dominican Republic) 7-5 (Estrella retired)
Denis Istomin (Uzbekistan) beat 4-Guillermo Garcia-Lopez (Spain) 6-2 7-5
Martin Klizan (Slovakia) beat Donald Young (U.S.) 7-6(4) 6-4
Edouard Roger-Vasselin (France) beat Jarkko Nieminen (Finland) 6-2 7-6(4)
1-Richard Gasquet (France) beat Bernard Tomic (Australia) 6-4 3-6 6-3
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- Caroline Wozniacki